Let A, B be two subsets of R and:  A+B:={ x+y : x E A, y E B}. A. Show that if A or B are open then A+B is open . B. Using sequences, Show that if A and B are compact  then A+B is compact.  C. Show that if A and B are closed A+B does not imply that A + B is.

Q: Let A and B be finite sets with A - B = {a, b, c, d, e, f, g} and An B = {h, i, j, k, l, m}. Find…

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Q: 4. For every given pairs of sets A and B below, determine whether A = B, or AC B, or BC A, or none…

A: As you post multiple question according to guideline I only have the first three please post the…

Q: Proposition 2.12. Suppose- that R is an equivalence relation on a set A, and let a, b e A. Then the…

A: Given below the detailed Solution

Q: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

Q: Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that(i) A × (B ∩ C) = (A ×…

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

Q: Theorem 5.25. Let A, B, and C be sets. Then 1. A× (B N C) = (A × B) N (A × C) 2. A × (B U C) = (A ×…

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Q: Suppose A and B are finite sets with |A| = a, |B| = b and |An B| = c. Find (a) |AB| (b) AX (AUB)|…

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Q: Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Give an example of three sets, A1, A2, and A3, such that…

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Q: 9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

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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: Broadly speaking, what is a mathematical closure? O A. Only relations have closures. They are…

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Q: Find the coordinate vector [x]B of the vector x relative to the given basis B. 23) b1 =| b2 and B =…

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Q: 3. Let A, B, C be sets. Provide a proof or a counterexample for each of the following statements. a.…

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

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Q: (ANB) –C= (A –C)NB.

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Q: (10) Prove that P(A)n P(B) is equal to P(An B) for any sets A and B. What can we say if the…

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Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.