Let A and B be sets. Show that (A × B) ∩ (B × A) = (A ∩ B) × (A ∩ B).

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A: Here we have to find the set D and E in list form.

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A: D= { } = empty set  n(D)= cardinality of set D

Q: Give an example of sets A and B for which |A U B| = |A|+|B|.

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Q: If ACB and BC A then A= B I F If A= B then Ax B= B× A. I F For any set A, fo(Ax B) = gɔ(A)× p(B) T F

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Q: Let A, B, and C be sets. Is the following equality true or false? A x (BUC) = (A × B) U (A × C')

A: Sets, distributive law

Q: Find u x v, v x u, and v x v. u = (3, -8, -3) (6, -6, -7) V = (a) u x v (b) v x u (c) v x v

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Q: Indicate whether the two sets are equal. D = {x: x is a natural number less than 3}, E = {1, 2, 3}

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Q: (B) = 10 and n(A N B) = 4, what is n(A u

A: n(A U B)=12

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

Q: Let a, b, c ∈Z+.    If  a | b and a | c then a | ( b + c )  true or false?

A: Use the definition of divisibility, to express b and c in terms of a. a|b⇒b=maa|c⇒c=na Therefore,…

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A: We want to define A x B

Q: Determine whether ⊂ , ⊆ , both, or neither can be placed in each blank to make the statement true.…

A: solution :      Given:    {P,Q,R,S} ____ {P,Q,R,S,T}To All above  '_____' by C , C or Nither

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Q: reasoning. G Is AHJF congruent to AFGH? Use a two-column proof to explain your F H

A: