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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 [ 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 [ i B i = [ i f 1 ( B i ) and f 1 \ i B i = \ i f 1 ( B i ). Solution. Absent....
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 Fall '11
 KeithCornell

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