Suppose F and G are families of sets. Prove that (UF)n (UG) ≤ U(F N G) iff VA EFVBE G(An BCU (FNG)).

Q: Prove that P(XY) = P(X)n P(Y) for all sets X and Y.

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Q: 60. Let A be a bounded subset of R. Which of these statements is/are not true about A? II: Vx € A,…

A: Option (B) is correct.

Q: 1. If f is a function on a set A = {1,2,3,4,5} such that f = {(1,2), (2,3), (3,4), (4, x), (5,5)}.…

A: Answer C

Q: Use the element method and contradiction to prove that for all sets S and T S Ռ ( T - S) = {  }

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Q: 5. Harry make the following argument about the set 2Z, the set of all even integers. Consider the…

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Q: Prove or disprove the statement There is no set S such that P(S) is denumerable.

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Q: (ii) for every singleton set A, m* (A) = 0.

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Q: Suppose A and B are bounded and nonempty subsets of real numbers and 1 E R. In this case: sup(A U B)…

A: Let A,B not empty, bounded subsets of R .Prove thatsup(A∪B)=max{sup(A),sup(B)}. Let: ⇒x∈A∪B⇒x∈A or…

Q: Let U be a universe and let A, B, C, D be any subsets of U. Prove or disprove the following…

A: Given U be a universe and let A, B, C, D be any subsets of U. We have to prove or disprove the…

Q: Let A and B be sets and suppose that A U B = B. Prove that ACB.

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Q: 2. Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. a)…

A: The solution of given problem is given as follows :

Q: al let (xt) betopology space and BCY then B is closed in y iff there is closed set CinX st B-COY

A: Let (X,Γ) be topology space and B⊂Y To Prove: B is closed in Y iff there is a closed set C in X s.t…

Q: F and Hare sets of real numbers defined as follows. F = {ww≤ 4} H = {w|w>5} Write FUH and FnH using…

A: We can find the union and intersection of sets in the below steps.

Q: Let A and Bbe subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N…

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Q: If X = {a, b, c} , Tx = {0, X, {a},{b, c}}, Y = {x, y, z} and ty = {Ø, Y, {y}} then f = {(a, z), (b,…

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Q: A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N B)…

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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: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

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Q: Prove that P(Sn T) P(S) n P(T) for any sets S and T

A: Let, S and T be a any set. also, P(S) be any power set of S and P(T) be any power set of T.x∈P(S∩T)…

Q: Let A and Bbe subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N…

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Q: let f and g be two bounded read - valu ed functions on the set ASR Showthat sup CPCX) +g X))s…

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Q: Let v be the set o all pairs of positive numbers (X,y) With two operations + and C denned as: (x1,…

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Q: A4For any two finite sets A and B, define f(A,B) to be the number of elements that are contained…

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Q: Suppose that A and B are sets and f : A –→ B is a function. Fix subsets X,Y C A. Prove that Imf(X) –…

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Q: 2. Let A, B and C be sets, and let g: A → B and f: B → C be functions. Prove: (i) If f, g are…

A: Answer given below.

Q: Give an example of a closed subset S of R2 such that conv S is not closed.

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Q: Let A, B be bounded subsets of R. Let A+B = {r+y:1 € A, y E B} and AB = {ry : 1 € A, y € B}. Which…

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Q: Let E and F be measurable sets each having finite measure. Prove that m(EAF) = 0 if and only if m(E)…

A: To prove: The statement "Let E and F be measurable sets each having finite measure. Then, mE∆F=0 if…