4. Let A and B be sets in a universe U. Consider the following two statements: i. P(AU B) ii. P(An B) =P(A)n P(B) Only one of these statements is always true. Decide which one it is, and prove it. Also give a counterexample to show that the other statement is false. P(A) U P(B)

Q: fer to the Venn diagram below. How many elements are in the set AUB? U A C n(AUB) = 22 12 36 50 3 B…

A: Solution

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A: It can be solved by the set theory

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Q: 2. Suppose A, B, and C are sets. Prove that (AUB) \C CAU (B \ C).

A: Introduction: We know that the difference property of two sets A and B as A/B=A∩B'.

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

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Q: Q3 ( Let A, B and C be sets. Show that (C – A)n (A – B) = 0, without using membership t %3D

A: Note: Sorry for the inconvenience but we are doing questions in text form because as per Bartleby's…

Q: 4. Using laws of set theory aided by two-column proof, show that AU (B – C) = (AU B) – (C – A). %3D

A: Solution As we know A-B = A ∩ Bc

Q: 7. (12 points) Use a proof by contradiction to prove: For all sets A, B, and C (A\C)n(B\C)n(A\B) = 0

A: Step 1: proof  let (A/C)∩(B/C)∩(A/B)=Φ this means ∃x∈(A/C)∩(B/C)∩(A/B) Step 2:⇒x∈A/C,x∈B/C,x∈A/B…

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Q: a) Let A = {4, 7, 8} and B = {−1, 5}, Find and compare sup(A+B) , inf(A+B), sup(A)+sup(B),sup A -…

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Q: Which of the following is NOT always true for sets A and B such that AC B? A. AnB = A C. BU (A - B)…

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Q: M=DThe letters in the Note: There Ore isord" mathematics- l elements in the set. b.) M-B when M is…

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A: Given below the detailed solution

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A: The true statements are:2456Explanation:

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A: GivenP(B)=14P(A∪B)=12P(A|B)=23

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A: Introduction A set can be defined as a collection of elements.

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A: Given proposition A≈B and C≈D By the bijection                                  f:A∪C → B∪DDefine…

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Q: Let A and B be sets with P(A) = P(B). Write a proof by contradiction to establish that A = B. [Note:…

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