Unformatted text preview: 2.16 (i) Let f : X → Y be a function, and let { S i : i ∈ I } be a family of subsets of X . Prove that f ³ [ i ∈ I S i ´ = [ i ∈ I f ( S i ). Solution. Absent. (ii) If S 1 and S 2 are subsets of a set X , and if f : X → Y is a function, prove that f ( S 1 ∩ S 2 ) ⊆ f ( S 1 ) ∩ f ( S 2 ) . Give an example in which f ( S 1 ∩ S 2 ) ±= f ( S 1 ) ∩ f ( S 2 ) . Solution. Absent. (iii) If S 1 and S 2 are subsets of a set X , and if f : X → Y is an injection, prove that f ( S 1 ∩ S 2 ) = f ( S 1 ) ∩ f ( S 2 ) . Solution. Absent. 2.17 Let f : X → Y be a function. (i) If B i ⊆ Y is a family of subsets of Y , prove that f − 1 ³ [ i B i ´ = [ i f − 1 ( B i ) and f − 1 ³ \ i B i ´ = \ i f − 1 ( B i ). Solution. Absent....
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 Fall '11
 KeithCornell
 Inverse function, Inverse trigonometric functions, Solution., inverse trig functions

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