Let A and B be sets with A ⊆ B and B transitive. Prove that P(A) ⊆ P(P(B)).

Q: Let A, B and C are sets. Prove that <= is transitive

A: For proving transitivity we need to show that if A&lt;=B and B&lt;=C then A&lt;=C

Q: 4. Prove that if A and B are convex sets, then AN B is also convex.

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Q: Prove that if A and B are transitive sets, then A ∪ B and A ∩ B are transitive sets

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Q: (2) Show that if f has support in a compact set A CR and g has support in a compact set B C R then f…

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Q: Prove that if A1,A2,…,An and B are sets, then (A1−B)∪(A2−B)∪⋯∪(An−B)=(A1∪ A2 ∪⋯∪ An)−B.

A: To Prove- Prove that if A1, A2, ...., An and B are sets, then A1 - B ∪ A2 - B ∪ .... ∪ An - B = A1 ∪…

Q: Prove that if A and B are sets, then P(A) U P (B) C P(AUB).

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Q: Suppose that A and B are finite sets. Prove that A U B is finite, and |A U B| = |A| +|B| -|A n B|.…

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Q: Show that if A and B are sets with AS B, then a) A UB-B. b) ANB-A.

A: Let A and B are two sets with A⊆B a) Let x∈A∪B which implies that x∈A or x∈B. Hence we can imply…

Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

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Q: Prove that if A is transitive set, then A+ is also a transitive set.

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Q: Let B and C be the subsets of some universal set X then prove that (C N B')' = BU C'

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Q: Find a counterexample to show that the statement is false. Assume all sets are subsets of a…

A: The solution is as shown below

Q: Đ A is a closed set.

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Q: Let C and D be subsets of a universal set U, then (C ∪ D) ⊆ (C ∩ D).

A: Given C and D are two subsets of universal set U.

Q: 2. Prove that if A, B,C are sets such that ANBNC = 0, then (A\B)n(C\B) = AnC. Prove that for onu got

A: Recall that, set A\B means a set of elements of A that does not belong to B.

Q: Prove formally that A\ B= A\(An B), for any sets A and B.

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Q: 4. Let A and B be sets. (a) If A and B are subsets of the same universal set U (so A × B is a subset…

A: The definition of complement is given at the end of proof

Q: A set is not open if its complement is not closed. O True O False

A: To find the given statement is true or false .

Q: Let C and D are be the subsets of some universal set U. Then D-C = C'nD is

A: We have to identify the statements as true or false.

Q: Let A and B be sets. Prove that the intersection of A and B is is a subset of the union between A…

A: To show that the elements which are common to both A and B belong to either A or B.

Q: If A C C and B C D then A U BC CU D.

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Q: - If C is Convex set ond a GR, then XC is a Convex set

A: Let C be a convex set and x∈R Then we have to show that xC is a convex set. The set xC is defined as…

Q: O (A x B) U (C x D) C (AUC) x (BUD)

A: Please check step 2 for the solution.!

Q: Let A and B be finite sets such that B = {b1, b2}. Prove that |A – B| < |A|.

A: We are given that A and B are two finite sets, where B= {b1, b2}.We have, |B| = 2, and let |A| =…

Q: Prove that if A is a set then so is {A}!

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Q: Write up a formal proof of the following: Claim: For any set A, A ⊆ A.

A: To prove rigorously that any set A is a subset of itself.

Q: uppose that ℱ is a non-empty family of sets, B is a set, and ∀A ∈ ℱ (A ⊆ B). Is ∪ℱ ⊆ B? Either…

A: Given: To explain the given statement as follows,

Q: If A and B are sets and A is a subset of B, then A and B cannot be disjoint.

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Q: Show that if A and B are sets with A ⊆ B, then a) A ∪ B = B. b) A ∩ B = A.

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Q: Prove that if R, S, and T are nonempty sets, then R×T ⊆ S×T if and only if R ⊆ S.

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Q: Use the element method for proving a set equals the empty set to prove that: For any A, B sets, (An…

A: Since you have post multiple question I only solve first one.

Q: Let A,B,C,D be sets. Prove that (A∩B)×(C∩D)=(A×C)∩(B×D)

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Q: Consider the following theorem of set theory: For any two sets A, B, [A U (B – A)] = A U B. a.…

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Q: 1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a…

A: This question is related to Set theory, We will solve it using given information.

Q: Prove or disprove that for all sets A, B, and C, we have a) A × (B ∪ C) = (A × B) ∪ (A × C). b) A ×…

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Q: For any sets A, B, C  use element argument to prove that  (A-B) - C is a subset of A - C

A: By the element argument we prove the given problem as follows :

Q: 3. Prove that if A is a set then so is {A} but do NOT use an argument that involves stages…

A: Let A is any set then as every set is a subset of itself then, A⊆A⇒A∈PA⇒A∈PPA

Q: Let A, B, and C be sets. Does A – C = B – C imply A = B? If so, prove it. If not, give a…

A: We have to give a counter example for  A – C = B – C imply A = B.

Q: Let A and B be two finite sets such that |A| = 20, |B| = 28 and |A U BI

A: Given A=20B=28A∪B=36

Q: Show that if A and B are finite sets, then A ∪ B is a finite set.

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Q: sets are subsets of a un

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Q: Let A, B, and C be sets. Prove that if A CB and B C C, then A C C.

A: Let, x belongs to A. Since, A is a subset of B, so, x belongs to A implies that, x belongs to B. So,…

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

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Q: Show that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

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Q: Let A, B be any sets with BCA. Then |P(B×B)[s|P(A×B)| O IP(AxB)|s|P(B×B)| O IP(AxB)|=|P(B×B)| O None…

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Q: Prove that for all sets A & B, (B-A) = A intersects B^c

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