4.1.4. (a) Prove A x B B x A. (b) Prove that if A C and B D then A x B C x D. Proof. (a) Define a mapping f : A × B → B × A by (a, b) → Need to show f is a bijection. We have f is one-to-one since f((a1, b1)) = f((a2, b2)) and For each (b, a) E B × A, we have (b) Since A C an B D, there exist bijections f : E A × B such that So f is onto. and g : Define a mapping h : by Show h is a below.

4.1.4. (a) Prove A x B B x A. (b) Prove that if A C and B D then A x B C x D. Proof. (a) Define a mapping f : A × B → B × A by (a, b) → Need to show f is a bijection. We have f is one-to-one since f((a1, b1)) = f((a2, b2)) and For each (b, a) E B × A, we have (b) Since A C an B D, there exist bijections f : E A × B such that So f is onto. and g : Define a mapping h : by Show h is a below.

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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