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Let f : A → B be a function between sets A and B. Let X1, X2 ⊆ A and Y1, Y2 ⊆ B. a) Prove that if X1 ⊆ X2, then f(X1) ⊆ f(X2). b) Prove that if Y1 ⊆ Y2, then f -1 (Y1) ⊆ f -1(Y2)

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

Let f : A → B be a function between sets A and B. Let X1, X2 ⊆ A and Y1, Y2 ⊆ B.

a) Prove that if X1 ⊆ X2, then f(X1) ⊆ f(X2).

b) Prove that if Y1 ⊆ Y2, then f ^-¹ (Y1) ⊆ f ^-¹(Y2)

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