1- (a) Given the set X = {A, B, C, D, E), find the number of permutations of the elements of X (b) Find the number of circular permutations of the elements of X. (c) What is the number of permutations if we choose only two of the elements of X ? (d) Find the number of permutations if the set is now X' = {A, E, A, D, E, E). Concider .

Q: Assume that the committee consists of 10 Republicans and 5 Democrats. A subcommittee consisting of 5…

A: Given Information: Assume that the committee consists of 10 Republicans and 5 Democrats. A…

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Suppose I had the set {1,2,3} and wanted to make a list of 5 of those elements that contained one…

A:

Q: Set A = {200, 400, 600} and Set B = {100, 300, 500, 700}.Determine the elements in A ∩ B'.    { }…

A: Please find the below attachment.Explanation:Step 1: Step 2: Step 3: Step 4:

Q: If a set has 8 elements, how many of its subsets have the given   numbers of elements?   (1) at…

A: Given that the total number of elements= 8  So the total number of subsets= 28=256   We can select…

Q: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

A: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

Q: Let A = {1,2} and B = {3, 4}. (a) Find A x B (b) How many subsets Ax B of size 2 are there? List…

A: Given that A= {1, 2} and B= {3, 4}A x B is the cartesian product

Q: If a(3, 4) – b(2, 4) = (8, 10), determine a and b.

A:

Q: If n(A ∪ B) = 97 and n(A) = n(B) = 66 find n(A ∩ B).

A: Given, n(A ∪ B) = 97 and n(A) = n(B) = 66

Q: The sum of the first n natural numbers, S = 1 + 2 + 3 + first n natural numbers is 171, determine…

A: Consider the given information:

Q: In a group of people, 68 people can speak English, 45 people can speak in Arabic and 19 people can…

A: It is given that 68 people can speak English, 45 people can speak Arabic and 19 people can speak…

Q: about the three subsets X1, X2, and X3 that partition a set X, except assume that the number of…

A: Let there are x elements in X2. So there are 6x elements in X1. There are 3x elements in X3. Given…

Q: Five lines are drawn in the plane. (a) What is the smallest number of points of intersection of the…

A: Given that - Five lines are drawn in the plane.

Q: Find Ax Bx C where A = {1,5}, B={13,17} , C={0}. O (1,13, 0), (1, 17, 0), (5, 13, 0), (17, 5, 0) O…

A:

Q: 5) For each + ive integer i, where i is equal to three, then find the union and intersection of…

A: 5 Given that Ai=x∈R|−1i<x<1i=−1i,1i. a We have to find the A1∪A2∪A3 and A1∩A2∩A3. Here,…

Q: Let A = {1,3} and B = {2,4}. (a) Draw a picture of the set A × B. (b) Compute P(A × B).

A:

Q: Let A = [1,2,3,4; 0,0,1,-1; 2,0,0,-3;1,2,2,5] Determine the rank of A.

A: Consider the given matrix A,