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).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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).

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