(a) Below is a Cayley table for the set S = {1,3,9, 21, 27} under diamond multiplication modulo 30. X30 1 3 1 3 9 21 27 1 3 9 21 27 vite gausu lluna (o) sono 3 9 27 3 21 9 9 27 21 9 3 21 21 3 9 21 27 27 27 21 3 27 9 SI is associative. vioo ei esina grivollol si to dose odlodw Bu oy tada atend to attuat For each of the four group axioms, state whether it is satisfied by (S, X30), briefly justifying your answer in each case. (b) Show that the binary operation o defined on the set R² by (a, b) o (c,d) = (c+d+ad, bd) Elisa & vd novig ai

Q: 5. Verify if the following are difference sets and state v, b, k, r, A for the ones that are: a)…

A: 5(a) Given that, (0,8,15,17,20,21)mod31 The cardinality of the set is 6 with mod31. Here V is the…

Q: Let S=(1,2,3,4,5,6,7,8). How many permutations are there if: a. The odd and even numbers trade…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: {x |x is even and 5 < x < 12} {5, 6, 7, 8, 9, 10, 11, 12} {6, 8, 10, 12} O {6, 8, 10} O There is not…

A: In roster form of set we have to list all elements of set.  So roster form of given set is { 6, ,8,…

Q: Let A = {1, 2, 3, .. ., 12} and let p.rand q permutations on A defined by p=(2,10,11), r= (3,6,5)…

A:

Q: Suppose that we have the set U={n: 0 <n < 100} of integer numbers as our universal set. Let P be the…

A: Given U = {n: 0≤n&lt;100} P be prime numbers in U E be even numbers in U F =…

Q: 6. Let s, be the number of different symmetric trains of length n which are built out of cars which…

A:

Q: 4. Six balls are thrown in four distinct squares. Represent the fundamental set N in the following…

A:

Q: 3. How many lists of length 3 can be made from the symbols A, B, C, D, E, F if... (a) repetition is…

A:

Q: Let the permutation is 3 2 1 4 then the next permutation is O a. 3- +2 -4 1- O b.-2 3-1 4- Oc. -2…

A: Given that, 3→←2←1 4→ The next permutation is, ←2 3 ←← 1 4 →

Q: I need help with these two questions.

A: Detailed explanation:

Q: 4) Let A and B are two sets as given below, show that A = B. A = {m EZ| m = 2a for some integer a}…

A: The given sets are:A=m∈ℤ m=2a for some integer aB=n∈ℤn=2b-2 for some integer bWe have to show that…

Q: 1. Let U= (xlx is a natural number and x ≤ 20), A=(2,3,5,7,9,12,19), B = (1,5,8, 9, 10, 15, 16, 18)…

A: We need to find the given sets

Q: If A's 1, 2, 3, 4, 5, B's' 1, 3, 4, 6', C's', '1', '6', '7'. Determines the elements of the…

A:

Q: Which of the following refers to the different arrangements of objects where some of them are the…

A: Permutation: Two different arrangements of objects where some of them are the same are identical are…

Q: 123 A SUKUEY OF 300 Kes IN BOSTON SHOWo THAT 142 EAT AT TACO BELL 102 EAT AT DEL TACO i 45 EAT A…

A: From athe given information we want to find the number

Q: C. A- (24.6, 8), B (2,3,7,9) and C (x3 I <9) are subsets of the universal set U(2,3.4.5, 6,7,8, 9).…

A:

Q: 3. Use PIE to find the number of arrangements of abcde such that there is NO appearance of…

A: Given :Usw PIE to the number of arrangments of abcde such that is NO appearanceof albhabetical…

Q: Let S = {1, 2, 3, 4, 5, 6, 7, 8}. (a) How many nonempty subsets of S are there? (b) How many subsets…

A: The given set is S=1,2,3,4,5,6,7,8. (a) We need to find the total number of nonempty subset of S.…

Q: In A, values of k for which det(A)=0 3 poi n are * (k-4 0 A = 0 k 3 k-1, O k=4, k=-3, k=-2 k=-4,…

A:

Q: 123 A SUKVEY OF 300 Kos IN bosTON SHOWE THAT 193 EAT AT TACO BELLa 102 EAT AT DEL TACO Í 45 EAT AT…

A: We have to find BC......

Q: 10. How many different Boolean functions are there of de- gree 7?

A:

Q: Refer to the Venn Diagram shown below. Find K - L'. K L 11 2 18

A: The given diagram is:

Q: 1. Which of the following pairs of sets are disjoint and which are not ? (i) {x:x is an even natural…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…