Exercise 3.4.6. Let A be a non-empty family of sets and let B be a set. (1) Prove that (U X∈A X)−B = U X∈A(X −B). (2) Prove that (∩ X∈A X)−B = ∩ X∈A(X −B).

Q: Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

A: (d) Let, x ∈ (A')'       => x ∉ A'       => x ∈ A      So, (A')' ⊆ A. . . . . . (I)…

Q: D. Let A, B, and C be subsets of some universal set U (a) If ANBC C and A° N B C C, prove that B CC

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Q: R= {(a,b)|a E T,b e T, a has higher GPA than b}. Why?

A: No, it is not a poset.  Since we know that a relation is a poset if the relation is…

Q: Prove that for any sets A, B, X - X − (An B) = (X − A) U (X – B). -

A: .

Q: Prove that P(A) NP(B) = P(ANB), where A and B are arbitrary sets

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Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Let U denote the set of all employees at Universal Life Insurance Company, and let T  =  {x  U | x…

A: T∪C=x:x∈T or x∈CT=x∈U|x drinks teaC=x∈U| x drinks coffeeT∪C=x:x drinks tea or coffee           =the…

Q: Let A and B be two measurable sets prove that if ASB then BIA is measurable and m(B\A)=m(B)-m(A)

A: The given problem is related with measure theory. Given that A and B are two measurable sets.  We…

Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

Q: (a) Let A, B be sets. Prove that A\(An B) = A\B. You may assume all sets in the question are…

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Q: 1) Let the set S be defined as S = {x | x is a U.S. President} Find n(S). 2) Define compliment to a…

A: use the basic property of sets .

Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

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Q: A={ y ∣ y ∈ N and 305< y ≤ 335} A has      subsets.  A has              proper subsets.

A: We have, A={ y ∣ y ∈ N and 305&lt; y ≤ 335} Let A and B be two sets. We say that A is a subset of B…

Q: Exercise 3.3.16. Prove or find a counterexample to the following statement. Let A, B and C be sets.…

A: Solution of the question is given below.

Q: exercise 1.4. Consider Z/24Z. Determine the set {5 . 1, 5 - 2, ...,5 · 23} =? where z is the class…

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Q: SETS Prove that X ⊆ Y if and only if X ∪ Y = Y.

A: Draw a sets of X and Y and plot different cases and check all conditions having XUY=Y.

Q: Let A and B be any sets. Show that: (a) A – B, B - A, and An B are disjoint with each other. (b) A =…

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Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Let A and B be nonempty sets. Prove that A x B = B x A if and only if A = B.

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Q: Exercise 3.3.20. Let A and B be sets. Suppose that BCA. Prove that AxA-BxB = [(A-B) XA]U[AX (A -…

A: We have B⊆A  first we prove that  AxA-BxB⊆  [Ax(A-B)]∪[(A-B)xA]   Then we prove that  AxA-BxB ⊇…

Q: 2. Prove for any sets A, B that (An B) = A if and only if A C B.

A: