Prove the following statements a. Let X and Y be nonempty sets and f: X→Y. If A⊆X and B⊆Y, then f[A]⋂B = f[A⋂f-1[B]]. (hint: f-1[B]={x∈X| f(x) ∈ B} b. Let A and B be nonempty sets and f: A→B and g: B→A. i. If f ∘ g is the identity function iB on B, then f is surjective. ii. If g ∘ f is the identity function iA on A, then f is injective

Prove the following statements a. Let X and Y be nonempty sets and f: X→Y. If A⊆X and B⊆Y, then f[A]⋂B = f[A⋂f-1[B]]. (hint: f-1[B]={x∈X| f(x) ∈ B} b. Let A and B be nonempty sets and f: A→B and g: B→A. i. If f ∘ g is the identity function iB on B, then f is surjective. ii. If g ∘ f is the identity function iA on A, then f is injective

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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