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

Q: Suppose that A, B, and C are sets. Prove that if AC B, then AnC C BN C. Disprove that if An C CBn C,…

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Q: If A and B are finite sets, then A ∪ B is also a finite set

A: Let A and B are finite sets. We need to show that , A ∪ B is also finite set. case 1) If A = B = ϕ A…

Q: Let A and B be two sets with a finite number of elements. Show that the number of elements in An B…

A: Given A and B are two finite sets. To show that the number of elements in A∩B plus the number of…

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: Let A, B, and C be sets. Show that (A − B) − C = (A − C) − (B − C).

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Q: Suppose that A and B are subsets of S. (a) Show that A ∩ B and A ∩ Bc are disjoint. (b) Express A as…

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Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if*

A: Let us consider four set A , B, C and D then AxC=BxD if all the elements of A are same as all the…

Q: display 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: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

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Q: Let A, B, C, and D be sets.

A: First, (AxC)U(BXD) ⸦(AUC) x(BUD)Take left hand side first , let  (x,y) ∈(AxC) U(BxD)=> (x,y)…

Q: Let A, B and C be arbitrary sets. Does it always hold that A ∪ (B × C) = (A ∪ B) × (A ∪ C) ?

A: No, this is not true in general. For example, consider the following :

Q: Suppose that A, B, and C are sets such that A ⊕ C = B ⊕ C. Must it be the case that A = B?

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Q: Give an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

A: We construct  an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

Q: prove the following statement If A, B, and C are sets, then A - (BnC) = (A - B) U (A - C). Suppose…

A: Since you have posted a question with multiple sub ports, we will provide the solution only to the…

Q: Show that for any sets A and B,A = ( A ∩ B ) ∪ ( A – B ) and                    A ∪ ( B – A ) = ( A…

A: Let A and  B be any two sets and U be the universal set.

Q: Let A, B, and C be sets. Use the the identity A − B = A ∩ B, which holds for any sets A and B to…

A: Identity Used: A-B=A∩BC Property Used: Intersection of sets is associative A∩(B∩C)=(A∩B)∩C

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: (AB) - C = (A − C) – (B − C).

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Q: For any sets A  B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B ∪ C). True or False.

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Q: Let A and B be sets. Prove that (A − B) ∩ (B − A) = ∅.

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