5. Prove that AUB=AnB either by giving a containment proof (that is, prove that the left side is a subset of the right side and that the right side is a subset of the left side) or by giving a membership table proof or using Venn diagram. 2

Q: Suppose we have 15 graphics cards and 4 servers. The graphics cards are all identical, but the…

A: Given that there are 15 graphics cards and 4 servers. All the graphic cards are identical, but the…

Q: 2. Find sets A, B, C, D such that the sets (AN B)U (C\ D), ((An B) U C) \ D, An(BUC) \ D, An(BU(C\…

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Q: 5.) There are three positions of programmers in a bank. Position I is the daytime programming…

A: We have three positions which is to filled with 15 candidates So for first position we have 15…

Q: 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B)U C) \ D, An(BU C) \ D, An(BU (C\…

A: Example of such set A,B,C,D are given below

Q: What is A ∪ B and A ∩ B when we let A = {11, 13, 15, 17, 19} and B = {12, 14, 16}? Show the Venn…

A: Given two sets A = {11, 13, 15, 17, 19} and B = {12, 14, 16} To find  A∪BA∩B and show its Venn…

Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

Q: 7. There is a SUNY-Korea party that n men and n women attended. Each ma knows exactly k women, and…

A: Men n Women m   Each woman knows exactly    k women k men Bipartite graph

Q: 7. If any subset of size five is chosen from {1, -1, 2, -2, 3, -3, 6, -6}, then prove that each of…

A: Given: Sample space={1,-1,2,-2,3,-3,6,-6} Subset of size 5 is chosen from sample space.

Q: 25. How many elements does each of these sets have where a and b are distinct elements? a) P({a,b,…

A:

Q: 5. Suppose that A = = {0,1} and B = {0}. (a) Write down the elements of AU B. (b) Write down the…

A: 5)(a) Suppose that and .     Thus, the power set of contains  elements. Recall the fact that : If…

Q: Prove that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) by giving a containment proof (that is, prove that the…

A:

Q: Suppose we have 15 graphics cards and 4 servers. The graphics cards are all identical, but…

A:

Q: 7. Consider the operation a * b = a + b – ab on the set S = Z. a) Is this operation commutative?…

A:

Q: A group of 40 Cabrillo students who were studying and/or being tutored in the HUB were surveyed and…

A: Venn Diagram is a diagrammatic representation to represent sets. The universal set is represented by…

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

A:

Q: Use inclusion-exclusion to find the number of ways to arrange the six numbers 1, 2, 3, 4, 5, 6 such…

A: please see the next step for solution

Q: Make a venn Diagram: In our classroom of 39 students, 11 students have a blue pen, 14 students have…

A: Total number of students = 39 No. of Students having only blue pen = 11 No. of Students having only…

Q: 2. Recall that, by definition, {A1, A2,..., An} = A if and only if every model of {A1, A2,..., An}…

A:

Q: Prove that at a party where there are at least two people, there are two people who know the same…

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Q: 3. In IT department, the students supposed to study three courses from Math section that is Calculus…

A:

Q: 1. Let U = {a, b, c, d,..., z}, A = {a, e, i, o, u, y}, and B = {m, a, t, h, e, i, c, s}. List the…

A: Given: U=a,b,c,d,…,z A=a,e,i,o,u,y B=m,a,t,h,e,i,c,s To find: A∪B A∩B A∩B¯

Q: 1. An aesthetic club has 100 members. Out of them 40 do dancing, 45 do music and 24 do drama. 15 do…

A: It is given as an aesthetic club with 100 members. Out of them 40 do dancing, 45 do music and 24 do…

Q: 2. A curious diner was observing her fellow customers. She noticed that, of the 27 customers she was…

A:

Q: a) An (B-C) c) (ANB) U (ANC) b) (ANB) U (ANC)

A:

Q: In a survey of 120 people it was found that 65 read news week magazine,45 read time,42 read…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: Let U = {q, r, s, t, u, v, W, x, y, z}, A = {q, s, u, w, y}, B= {q, s, y, z}, and C= {v, w, x, y,…

A: To determine the elements of the set shown below.

Q: Choose the small world that shows the following interference is NOT valid: (∀x)(Fx->Gx) and Fa;…

A: Given that ∀x(Fx→Gx) and Fa therefore ∀xGx The individuals are a,b Then the predicates are,…

Q: How many elements are in the set S = {∅, x, y, {x}, {{y}}, {x, {y}}, {x, {x}, {{y}}}}

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

Q: 2. Prove or disprove 1. forall A, B,C, A(BUC) C ABUAC 2. forall A, B,C, A(BUC) 2 ABUAC 3. forall A,…

A:

Q: Find the probability that a randomly selected member either does dancing or music. b) Find whether…

A: An aesthetic club has 100 members. Out of them 40 do dancing, 45 do music and 24 do drama. 15 do…

Q: Let U={1,2,3,...,10}, A={1,3,5,7}, B={1,2,3,4}, and C={3,4,6,7,9}. Find  a. A ∩ B b. A ∩ (B' U…

A: Introduction:    The set operations are performed on two or more sets to obtain a combination of…

Q: What is the minimum number of students required in a discrete structures class to be sure that at…

A: As we have five grades: k=5 And the number of students: r=9 And we have to calculate: Nk=r N5=9