Exercise 3.4.7. Let I be a non-empty set, let {Ai}i∈I be a family of sets indexed by I and let B be a set. (1) Prove that B×(U i∈I Ai) = U i∈I(B×Ai). (2) Prove that B×(∩ i∈I Ai) = ∩ i∈I(B×Ai).

Exercise 3.4.7. Let I be a non-empty set, let {Ai}i∈I be a family of sets indexed by I and let B be a set. (1) Prove that B×(U i∈I Ai) = U i∈I(B×Ai). (2) Prove that B×(∩ i∈I Ai) = ∩ i∈I(B×Ai).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 29E

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Question

Exercise 3.4.7. Let I be a non-empty set, let {Ai}i∈I be a family of sets indexed by
I and let B be a set.
(1) Prove that B×(U i∈I Ai) = U i∈I(B×Ai).
(2) Prove that B×(∩ i∈I Ai) = ∩ i∈I(B×Ai).

Expert Solution