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: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  In how many ways can…

A: Permutation: A permutation is an arrangement of objects in a definite order. Let n is the total…

Q: Find the dimension of the set S= {(2, 4), (4, 8)}?

A: The dimension of the set S can be find out by finding the linearly independent vectors in it.…

Q: The set {[1 -1 3], [2 3 -2], [3 2 1], [0 0 0]} spans صواب İhi

A:

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: 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: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are %3D %3D two sets. find R = {(x, y): x E X and y E Y…

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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: (b) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 and 8 such…

A: Given Digits: 0,1,2,3,4,5,6,7 & 8

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: Determine n(U), the number of elements in the universal set, given n(X) = 47 and n(X′) = 156.

A: Note : {X, X'} forms a partition of U. i.e. X & X' are disjoint and their union is the universal…

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: 2. Consider S3 = the set of all permutations on the set [3]. You can find these 6 permutations in…

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

Q: d) The set E = (-1,0) U (0, 1] is an open set. %3D

A: Given set is E = (-1, 0) ∪ (0, 1]

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: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

A:

Q: . Let f= {(-4,4), (-2, 4), (1, 3), (3, 5), (4, 6)} and g= {(-4, 2), (-2, 1), (0, 2), (1, 2), (2, 2),…

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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,{{1,2}}}. Find the power set P(A)

A:

Q: Suppose a die is cast 10 times. Let X1 be the number of terminations in the set {1, 2}, X2 be the…

A: Let us assume X1 denotes {1,2} faces show in 10 throw . The probability of that will be P(X1=1 and…

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,

Q: There are twenty marbles of similar colour and size where each marble is labelled with a number from…

A: Number of marbles in total =20. Number of marbles with even number =10.  number of marbles with odd…

Q: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  Show that the number…

A: Consider that G is the group of females and B is the group of males.This two group of G and B can be…