Addition and multiplication table for z6

And a school-going pupil who knows simple addition and subtraction (of single-digit numbers) and the multiplication-table up to five times five, can improvise all the necessary multiplication-tables for himself at any time and can himself do all the requisite multiplications involving bigger multiplicands and multipliers, with the aid of the ...The addition rule for such pairs is (a, b) + (c, d) = (a+c, b+d) and the multiplication rule is (a,b) (c,d) = (ac, bd). If R1 and R2 are rings, then R1 x R2 is also a ring, as you could show by checking that all the axioms hold. Take as a concrete example R1 = Z2 and R2 = Z3. Then Z2 x Z3 has as elements the 6 pairs 00, 01, 02, 10, 11, 12.Now we are sowing the table and table we can now here is the table, this is X six and this is the zero, this is one, this is 234 and five, four and five. This is the five. This is zero, this is one, ... Construct addition and multiplication tables for Z6. b. Compute 1! +2!+3+ 4 2021! (mod 30). (Note the factorials!) is antarctica an island Dec 16, 2017 · We consider the ring Z4. Construct a table which describes the addition of all elements in the ring with each other: Construct the multiplication table for \(\mathbb{Z}_4\). Construct the addition and multiplication tables for \(\mathbb{Z}_5\). Construct the addition and multiplication tables for \(\mathbb{Z}_6\). dr axe collagen tbn Step #1: We’ll label the rows and columns with the elements of Z 5, in the same order from left to right and top to bottom. Step #2: We’ll fill in the table. Each entry is the result of adding the row label to the column label, then reducing mod 5. Features of Cayley Table –. Every row and column of the table should contain each element ...insert data from one table to another in laravel. path of titans map; tesamorelin peptide. belmar beach cam 16th ave; q skills for success reading and writing 5 pdf free download; nhtsa report. ukraine news fox; beaufort south carolina; body found in oklahoma river; bainbridge ga; kohler 7000 series 24 hp oil type. 4 letter words from burial cpc exam questions and answers pdf 2022 Kevin James MTHSC 412 Section 2.6 {Congruence Classes. Theorem 1 Addition is a well de ned binary operation on Z n. ... From the multiplication table for Z 6, we see that [2];[3] and [4] are zero divisors in Z 6. Kevin James MTHSC 412 Section 2.6 {Congruence Classes. The set of all 2\( \times \)2 matrices over the field of real number under the usual addition and multiplication of matrices is A). not a ring B). a ring with unity. ssc cpo question paper 2019 pdf. vishwaroopam movie download moviesda. 3d warehouse 2013; jewsons drainage; minnal murali movie download telegram ... skate 3 free download pc full versionMathematical Methods for Physicists 7th Ed Arfken solutions manual jessica rabbit bdsm Example 44 The addition and multiplication tables for Z4 are: ... Note that the addition table has a cyclic pattern, while there is no.Cayley Table Properties. The Cayley table gives all the information needed to understand the structure of a group. From the Cayley table for this group, we see what the elements are: 0, 1, and 2.14.3 Modular Addition and Multiplication . In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary operations on the sets Z n = { 0, 1, 2, , n − 1 } where n ∈ N based on the addition and multiplication of integers. Notice from the table 5 + 5 = 4. This seems strange in the usual sense of addition we are used to, but notice that in mod 6 this is true. In fact, 5 + 5 = 10, and we know that 10 is congruent to 4 (mod 6). So, it is true 5 + 5 does actually equal 4! Similarly the table above tells us 5 * 5 = 1. 14.3 Modular Addition and Multiplication . In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary operations on the sets Z n = { 0, 1, 2, , n − 1 } where n ∈ N based on the addition and multiplication of integers. Kevin James MTHSC 412 Section 2.6 {Congruence Classes. Theorem 1 Addition is a well de ned binary operation on Z n. ... From the multiplication table for Z 6, we see that [2];[3] and [4] are zero divisors in Z 6. Kevin James MTHSC 412 Section 2.6 {Congruence Classes. vail invitational 2022 soccer Write out the addition and multiplication tables for Z6 (where by addition and multiplication we mean +6 and 6). 2. Let f : Z? –→ Z² be given by f (m,n) = (m-n,n). The composite functions fk, for k e Z+, are defined as fi (m, n) = f (m,n), and fk+1 (m,n) = f (fr (m, n)), for k e Z*. Addition and Multiplication Tables. tables. 16,027 Solution 1.And a school-going pupil who knows simple addition and subtraction (of single-digit numbers) and the multiplication-table up to five times five, can improvise all the necessary multiplication-tables for himself at any time and can himself do all the requisite multiplications involving bigger multiplicands and multipliers, with the aid of the ...Dec 16, 2017 · We consider the ring Z4. Construct a table which describes the addition of all elements in the ring with each other: Construct the multiplication table for \(\mathbb{Z}_4\). Construct the addition and multiplication tables for \(\mathbb{Z}_5\). Construct the addition and multiplication tables for \(\mathbb{Z}_6\). Aug 02, 2017 · Example 6.4. The addition and multiplication tables for Z 6 are: + 01 234 5 0 01 234 5 1 12 345 0 2 23 450 1 3 34 501 2 4 45 012. 1) =x2+4x+6x+4ツ「6(ツ。1 = 6 in Z 7) =x2ツ。3x+6x+3(ツ。1 = 6 in Z 7) =x2+3x+3 =x2ツ。4x+3: So it seems the factoring technique might work. symptoms of soul ties Write out the addition and multiplication tables for Z6 (where by addition and multiplication we mean +6 and 6). 2. Let f : Z? –→ Z² be given by f (m,n) = (m-n,n). Integer Partitioner. Letter Frequency Analyser. Mandelbrot Set Orbit Tracer. One Variable Statistics Calculator. Pascal's Triangle Generator. Polygon Calculator. Programming. ASCII Table Lookup. Keyboard Event Tester. pokemon heartgold action replay codes We can see an example of the third difference in the multiplication table for Z 5,where3 and 2 are multiplicative inverses, since 3 · 2=2· 3 = 1. To illustrate the first two of these differences, we look at Z 6. Example 6.4. The addition and multiplication tables for Z 6 are: + 01 234 5 0 01 234 5 1 12 345 0 2 23 450 1 3 34 501 2 4 45 012.Cayley Table Properties. The Cayley table gives all the information needed to understand the structure of a group. From the Cayley table for this group, we see what the elements are: 0, 1, and 2.Keywords: abacus course, arithmetic computation, developmental dyscalculia, mathematical cognition, mathematics learning disability lost all my money trading reddit 14.3 Modular Addition and Multiplication . In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary operations on the sets Z n = { 0, 1, 2, , n − 1 } where n ∈ N based on the addition and multiplication of integers. The first four of these axioms (the axioms that involve only the operation of addition) can be sum-marized in the statement that a ring is an Abelian group (i.e., a commutative group) with respect to the operation of addition. Example. The set Z of integers is a ring with the usual operations of addition and multiplication. Example.Example 44 The addition and multiplication tables for Z4 are: ... Note that the addition table has a cyclic pattern, while there is no. mini cooper jbe programming If we divide six by six we will get the remainder at zero. So I'm going to put a zero here two plus zero. I mean two plus 0 to 2 plus 132 plus 42 plus 242 plus 352 plus four which is six. Again divide six by six. We got the remainder at 60 and two plus five which is 77 divided by six. We will get the remainder as one. Identity 0∈H 21+3=4=0 1 and 3 are inverse of each other and they belong to H 2∴ inverse exist for every element of H 2 and also, closure property is satisfied as 1+3=0,0+3=3,0+1=1∈H 2Thus, H 2 is a proper subgroup of (Z 4,+). If we divide six by six we will get the remainder at zero. So I'm going to put a zero here two plus zero. I mean two plus 0 to 2 plus 132 plus 42 plus 242 plus 352 plus four which is six. Again divide six by six. We got the remainder at 60 and two plus five which is 77 divided by six. We will get the remainder as one. Answer (1 of 2): What is this [email protected] here? Why another binary operation, when addition and multiplication operations are already there ?2022. 2. 14. ... VIDEO ANSWER:In the question consider, said Jed six considered said J. L six difficult to 012 three, four and 5. four and 5. roblox client side exploit The addition table is complete and the multiplication table is not. The instructions say to use the distributive laws, but I can't seem to find the solutions using the distributive laws. The instructions say to use the distributive laws, but I can't seem to find the solutions using the distributive laws. spn 625 fmi 9 bendix Official City of Calgary local government Twitter account. Keep up with City news, services, programs, events and more. Not monitored 24/7.We can see that Z 5 has multiplicative inverses, because every element other than 0 has a 1 somewhere in its row in the multiplication table. So 1 -1 = 1, 2 -1 = 3, 3 -1 = 2, and 4 -1 = 4. On the other hand, Z 4 is not a field because 2 has no inverse, there is no element which gives 1 when multiplied by 2 mod 4.Indeed, if we relabel each entry nin the rst set of tables with the ordered pair corresponding to its reduction modulo 2 and 3 (so that 1 becomes (1;1), 2 becomes (0;2), and so forth) we will obtain the second set of tables!. Write the addition and multiplication tables for \mathbb {Z}_ {6} Z6. Explanation Verified Reveal next step Reveal all steps Create a free account to see explanations Continue with Google Continue with Facebook Sign up with email Recommended textbook solutions Advanced ... medium beasts 5e 14.3 Modular Addition and Multiplication. 🔗. In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary operations on the sets Z n = { 0, 1, 2, …, n − 1 } where n ∈ N based on the addition and multiplication of integers. For a and b in Z n we consider ( a ...We can see that Z 5 has multiplicative inverses, because every element other than 0 has a 1 somewhere in its row in the multiplication table. So 1 -1 = 1, 2 -1 = 3, 3 -1 = 2, and 4 -1 = 4. On the other hand, Z 4 is not a field because 2 has no inverse, there is no element which gives 1 when multiplied by 2 mod 4.Get the addition tables from 1 to 10 and register with BYJU'S - The Learning ... For more related topics on addition, subtraction and multiplication tables, ... touch vpn free unlimited mod v1 5 0 unlocked androgeek88 com Dec 16, 2017 · We consider the ring Z4. Construct a table which describes the addition of all elements in the ring with each other: Construct the multiplication table for \(\mathbb{Z}_4\). Construct the addition and multiplication tables for \(\mathbb{Z}_5\). Construct the addition and multiplication tables for \(\mathbb{Z}_6\). Find all invertible elements in Z5. 12 a) Let R be a commutative ring. Show that the cancellation law with respect to multiplication holds in R if and only if a , b ? R, ab = 0? either a = 0 or b = 0. b) Prepare a multiplication modulo 6 table for a ring ( Z6 , +6 , ×6). fake call app download multiplication table for these elements: e a b e e a b a a b e b b e a Since all the elements of this table are in H1, it follows that H1 is closed under the multiplication on S4. Moreover, the identity of S4, namely (1), is in H1, and a¡1 = b, b¡1 = a so H 1 is closed under inverses. Hence, H1 is a subgroup of S4. J Math 4200 October 26, 2009 1. multiplication table for these elements: e a b e e a b a a b e b b e a Since all the elements of this table are in H1, it follows that H1 is closed under the multiplication on S4. Moreover, the identity of S4, namely (1), is in H1, and a¡1 = b, b¡1 = a so H 1 is closed under inverses. Hence, H1 is a subgroup of S4. J Math 4200 October 26, 2009 1. 10 inch exhaust fan with shutter Now we are sowing the table and table we can now here is the table, this is X six and this is the zero, this is one, this is 234 and five, four and five. This is the five. This is zero, this is one, ... Construct addition and multiplication tables for Z6. b. Compute 1! +2!+3+ 4 2021! (mod 30). (Note the factorials!)Answer (1 of 2): What is this [email protected] here? Why another binary operation, when addition and multiplication operations are already there ? red light area quotes Find all invertible elements in Z5. 12 a) Let R be a commutative ring. Show that the cancellation law with respect to multiplication holds in R if and only if a , b ? R, ab = 0? either a = 0 or b = 0. b) Prepare a multiplication modulo 6 table for a ring ( Z6 , +6 , ×6). polynomial addition and multiplication with coefficient arithmetic performed in the field F. The set (R,+,·,0 R,1 R) is called the ring when all the requirements of the Definition 1 except the 6-th item are satisfied. It is easy to see F[x] is a ring. Note 11. The indeterminate x in a polynomial f(x) ∈ F[x] is not an element of the field.The Operation Table as Metaphor in Learning Abstract Algebra (Paper to be ... Wendy's tables for addition and multiplication in Z6 x 0 1 2 3 4 5. army m17 qualification standards 2022 Notice from the table 5 + 5 = 4. This seems strange in the usual sense of addition we are used to, but notice that in mod 6 this is true. In fact, 5 + 5 = 10, and we know that 10 is congruent to 4 (mod 6). So, it is true 5 + 5 does actually equal 4! Similarly the table above tells us 5 * 5 = 1. Write out the addition and multiplication tables for Z6 (where by addition and multiplication we mean +6 and 6). 2. Let f : Z? –→ Z² be given by f (m,n) = (m-n,n). 1. Write down the addition and multiplication table for Z/5Z. All classes should be written in terms of their canonical representative (unique representative between 0 and 4). 2. Suppose a = a' mod n and b = b' mod n. (a) Show that a + b = a' + b'...long anal sex videos; plus size boutique baton rouge guadalupe river paddling trail guadalupe river paddling trail Identity 0∈H 21+3=4=0 1 and 3 are inverse of each other and they belong to H 2∴ inverse exist for every element of H 2 and also, closure property is satisfied as 1+3=0,0+3=3,0+1=1∈H 2Thus, H 2 is a proper subgroup of (Z 4,+). tesla two button reset May 12, 2018 · 3 Answers. F 4 is the finite field of order 4. It is not the same as Z 4, the integers modulo 4. In fact, Z 4 is not a field. F 4 is the splitting field over F 2 = Z 2 of the polynomial X 4 − X. You get the addition table by observing that F 4 is a 2-dimensional vector space over F 2 with basis 1 and x where x is either of the roots of X 4 ... In this case, our fixed modulus is 6, so we say "mod 6." Here, operations of addition and multiplication with integers will result in a number that is ... Notice above that both 10 and 28 are congruent to 4 in mod 6. So, we can use Microsoft Excel to generate tables to describe addition and multiplication in mod 6. Notice how the only ... cisco switch aaa radius configuration example Answer: The set of representatives of the elements of \mathbb{Z}/6\mathbb{Z} is \{0,1,2,3,4,5\}. All you need to do is find the smallest value k>0 such that: x^k=1 \pmod 6 for each of these representatives. You should be able to find the (multiplicative) order of 1 …polynomial addition and multiplication with coefficient arithmetic performed in the field F. The set (R,+,·,0 R,1 R) is called the ring when all the requirements of the Definition 1 except the 6-th item are satisfied. It is easy to see F[x] is a ring. Note 11. The indeterminate x in a polynomial f(x) ∈ F[x] is not an element of the field.14.3 Modular Addition and Multiplication . In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary … indian female singers with short hair Answer: The set of representatives of the elements of \mathbb{Z}/6\mathbb{Z} is \{0,1,2,3,4,5\}. All you need to do is find the smallest value k>0 such that: x^k=1 \pmod 6 for each of these representatives. drake middle school scandalmultiplication table for these elements: e a b e e a b a a b e b b e a Since all the elements of this table are in H1, it follows that H1 is closed under the multiplication on S4. Moreover, the identity of S4, namely (1), is in H1, and a¡1 = b, b¡1 = a so H 1 is closed under inverses. Hence, H1 is a subgroup of S4. J Math 4200 October 26, 2009 1. 14.3 Modular Addition and Multiplication . In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary operations on the sets Z n = { 0, 1, 2, , n − 1 } where n ∈ N based on the addition and multiplication of integers. jackson ms shooting 2022 Keywords: abacus course, arithmetic computation, developmental dyscalculia, mathematical cognition, mathematics learning disability tj maxx returns long anal sex videos; plus size boutique baton rouge guadalupe river paddling trail guadalupe river paddling trail 2005. 4. 21. ... [x]+[y]=[x + y];. [x] · [y]=[x · y]. As an example, tables 1 and 2 show the addition and multiplication tables for Z5 and Z6 respectively.From the addition and multiplication tables, we can readily read tables for additive and multiplicative inverses: additive inverse 0 0 1 4 2 3 3 2 4 1 multiplicative denoising autoencoder pytorch github long anal sex videos; plus size boutique baton rouge guadalupe river paddling trail guadalupe river paddling trail Example 4.1. (a) The set R of real numbers, with the usual addition and multiplication, is a field. (b) ThesetCofcomplexnumbers,withtheusual addition andmultiplication, is a field. 3 (c) The set Qof rational numbers, with the usual addition and multiplication, is a field. (d) The set Zof integers, with the usual addition and multiplication ...14.3 Modular Addition and Multiplication . In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary operations on the sets Z n = { 0, 1, 2, , n − 1 } where n ∈ N based on the addition and multiplication of integers. valet key wont start car Keywords: abacus course, arithmetic computation, developmental dyscalculia, mathematical cognition, mathematics learning disabilityExplanation: Cayley tables are two dimensional grids describing the results of addition or multiplication of all elements in a group. In the case of a ring such as Z7, there are separate tables for addition and multiplication. Here is the table for addition:Dec 16, 2017 · We consider the ring Z4. Construct a table which describes the addition of all elements in the ring with each other: Construct the multiplication table for \(\mathbb{Z}_4\). Construct the addition and multiplication tables for \(\mathbb{Z}_5\). Construct the addition and multiplication tables for \(\mathbb{Z}_6\). aqha youth world show live stream Write out the addition and multiplication tables for Z6 (where by addition and multiplication we mean +6 and 6). 2. Let f : Z? –→ Z² be given by f (m,n) = (m-n,n). Find all invertible elements in Z5. 12 a) Let R be a commutative ring. Show that the cancellation law with respect to multiplication holds in R if and only if a , b ? R, ab = 0? either a = 0 or b = 0. b) Prepare a multiplication modulo 6 table for a ring ( Z6 , +6 , ×6). Construct the addition and multiplication tables for ℤ6. ... There are elements in ℤ4 and ℤ6 without a multiplicative inverse. Which elements are these? redline roleplay discord We begin by examining linear equations. Solving Linear Equations Before reading on, flip over to page 7 where the addition and multiplication tables for Z6 and ...long anal sex videos; plus size boutique baton rouge guadalupe river paddling trail guadalupe river paddling trail 2005. 4. 21. ... [x]+[y]=[x + y];. [x] · [y]=[x · y]. As an example, tables 1 and 2 show the addition and multiplication tables for Z5 and Z6 respectively.Dec 16, 2017 · We consider the ring Z4. Construct a table which describes the addition of all elements in the ring with each other: Construct the multiplication table for \(\mathbb{Z}_4\). Construct the addition and multiplication tables for \(\mathbb{Z}_5\). Construct the addition and multiplication tables for \(\mathbb{Z}_6\). sarasota county sheriff patrol zones Identity 0∈H 21+3=4=0 1 and 3 are inverse of each other and they belong to H 2∴ inverse exist for every element of H 2 and also, closure property is satisfied as 1+3=0,0+3=3,0+1=1∈H 2Thus, H 2 is a proper subgroup of (Z 4,+). Make Addition and Multiplication Tables . With Inactive, it is easier than ever to create tables of values. An addition table for the numbers 1 through 7. In[1]:= X. Out[1]//TableForm= A multiplication table for the numbers 1 through 7. In[2]:= X. Out[2 ...Purple acid phosphatases (PAPs) are a group of metallohydrolases that contain a dinuclear Fe(III)M(II) center (M(II) = Fe, Mn, Zn) in the active site and are able to catalyze the hydrolysis of a variety of phosphoric acid esters. real katana set Addition and multiplication table for z6. how does strattera make you feel reddit. st petersburg population 2022 victorious x male reader vinyl cutter software free ... addition and multiplication table for z6. arm protectors for thin skin. review complex exam no longer needed. professor messer a 1001 course notes pdf free download. ... and +towgs84/+nadgrids terms will be missing most of the time +proj=longlat +ellps=WGS84 +datum=WGS84 +no defs Table: SRID table entry SRID is referenced by an integer, [2000, ...Find all invertible elements in Z5. 12 a) Let R be a commutative ring. Show that the cancellation law with respect to multiplication holds in R if and only if a , b ? R, ab = 0? either a = 0 or b = 0. b) Prepare a multiplication modulo 6 table for a ring ( Z6 , +6 , ×6). Finite Group Z6 One of the two groups of Order 6 which, unlike , is Abelian. It is also a Cyclic. It is isomorphic to . Examples include the Point Groups and , the integers modulo 6 under addition, and the Modulo Multiplication Groups , , and .Example 44 The addition and multiplication tables for Z4 are: ... Note that the addition table has a cyclic pattern, while there is no.Write out the addition and multiplication tables for Z6 (where by addition and multiplication we mean +6 and 6). 2. Let f : Z? –→ Z² be given by f (m,n) = (m-n,n). infj boyfriend distant Find all invertible elements in Z5. 12 a) Let R be a commutative ring. Show that the cancellation law with respect to multiplication holds in R if and only if a , b ? R, ab = 0? either a = 0 or b = 0. b) Prepare a multiplication modulo 6 table for a ring ( Z6 , +6 , ×6).Notice from the table 5 + 5 = 4. This seems strange in the usual sense of addition we are used to, but notice that in mod 6 this is true. In fact, 5 + 5 = 10, and we know that 10 is congruent to 4 (mod 6). So, it is true 5 + 5 does actually equal 4! Similarly the table above tells us 5 * 5 = 1. Write out the addition and multiplication tables for Z6 (where by addition and multiplication we mean +6 and 6). 2. Let f : Z? –→ Z² be given by f (m,n) = (m-n,n). table. Similarly, the symmetry of the multiplication table implies that multiplication is commutative for this set. From the addition table it is also clear ... low income housing for single moms The addition table is complete and the multiplication table is not. The instructions say to use the distributive laws, but I can't seem to find the solutions using the distributive laws. The instructions say to use the distributive laws, but I can't seem to find the solutions using the distributive laws. 14.3 Modular Addition and Multiplication . In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary operations on the sets Z n = { 0, 1, 2, , n − 1 } where n ∈ N based on …8 Input / Output Charts for students to complete Prior knowledge of patterns, addition, subtraction, multiplication and division are required to complete this lesson. Hope this helps =) What's My Rule?: Input and Output Tables by Felisa Williams is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. bariatric wheelchair navient student loans settlement center console for police interceptor The set of all 2\( \times \)2 matrices over the field of real number under the usual addition and multiplication of matrices is A). not a ring B). a ring with unity. ssc cpo question paper 2019 pdf. vishwaroopam movie download moviesda. 3d warehouse 2013; jewsons drainage; minnal murali movie download telegram ...Aug 02, 2017 · Example 6.4. The addition and multiplication tables for Z 6 are: + 01 234 5 0 01 234 5 1 12 345 0 2 23 450 1 3 34 501 2 4 45 012. 1) =x2+4x+6x+4ツ「6(ツ。1 = 6 in Z 7) =x2ツ。3x+6x+3(ツ。1 = 6 in Z 7) =x2+3x+3 =x2ツ。4x+3: So it seems the factoring technique might work. 14.3 Modular Addition and Multiplication . In Section 3.4 we have encountered the addition of hours, weekdays, and months as an example for modular arithmetic. We now introduce binary operations on the sets Z n = { 0, 1, 2, , n − 1 } where n ∈ N based on the addition and multiplication of integers. 10600 central ave se albuquerque nm Write out the addition and multiplication tables for Z6 (where by addition and multiplication we mean +6 and 6). 2. Let f : Z? –→ Z² be given by f (m,n) = (m-n,n). Compute the addition and multiplication tables for Z3 and Z6. 2. Calculate the elements of U6 and U8 and draw a picture of them.Dec 16, 2017 · We consider the ring Z4. Construct a table which describes the addition of all elements in the ring with each other: Construct the multiplication table for \(\mathbb{Z}_4\). Construct the addition and multiplication tables for \(\mathbb{Z}_5\). Construct the addition and multiplication tables for \(\mathbb{Z}_6\). romance book signings 2023