3. Suppose that X and Y are two sets and f: X → Y is a function. Prove each of the following: (i) If A and B are two subsets of X and A C B, then ƒ(A) C ƒ(B). (ii) If {Hala e A} is an indexed family of subsets of X, then f(UaEAHa) = Uae^ƒ (Ha). (iii) If {Gala e A} is an indexed family of subsets of Y, then f-¹ (naEAGα) = nae^ f-¹(G₁).
3. Suppose that X and Y are two sets and f: X → Y is a function. Prove each of the following: (i) If A and B are two subsets of X and A C B, then ƒ(A) C ƒ(B). (ii) If {Hala e A} is an indexed family of subsets of X, then f(UaEAHa) = Uae^ƒ (Ha). (iii) If {Gala e A} is an indexed family of subsets of Y, then f-¹ (naEAGα) = nae^ f-¹(G₁).
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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Transcribed Image Text:3. Suppose that X and Y are two sets and f: X Y is a function.
Prove each of the following:
(i) If A and B are two subsets of X and AC B, then f(A) C ƒ(B).
(ii) If {Hala e A} is an indexed family of subsets of X, then
f(UaEAH₂) = Uae^f (Ha).
(iii) If {Gala e A} is an indexed family of subsets of Y, then
f-¹(naEAGα) = nae^ f-¹(Ga).
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