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Solutions15

# Solutions15 - Chapter 15 Hints and Selected Solutions...

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Chapter 15: Hints and Selected Solutions Section 15.1 (page 411) 15.1 Hint: The exercise is to test your understanding of the axiom of exten- sionality. According to that axiom, sets are identical if and only if they have the same members, regardless of how the members are listed. In particular, the order in which they are listed is irrelevant, as is the num- ber of times a member gets list. For example. { 2 , 3 , 2 } = { 2 , 3 } = { 3 , 2 } . 15.2 1. { 7 , 11 , 13 } 4. Hint: This will be a set with only one word in it. The word de- scribes a kind of person with lots of buzz about them. 15.3 1. 19 , 29 , 31, for example. You should not list the same three. 4. pseudo , un , pre , for example. 15.5 Here is a proof of the argument: 1

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Section 15.2 (page 414) 15.7 1. True, since it only citizens are eligible for election to the senate. 4. True, since John’s brothers are among his relatives. 7. False. The quotes mean that the members of the sets are numerical terms, numbers. The numeral “2” is in the first set, not in the second, for example. 2
15.13 Section 15.3 (page 418) 15.14 We have filled in the first 11 steps of Proof Intersection 1 below: 3

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15.15 1. { 2 , 4 } 4. {} (the empty set) 7. { 2 , 3 , 4 , 5 } 15.17 We first show a proof of 15.17 under construction. Notice that at step 5 we are just about to use a default instance of Elim . The completed proof is shown below. 4
15.21 We want to give an informal proof of a ( b c ) = ( a b ) ( a c ). By Proposition 3, it suffices to prove a ( b c ) ( a b ) ( a c ) and ( a b ) ( a c ) a ( b c ). We prove the first part, leaving the second to you.

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Solutions15 - Chapter 15 Hints and Selected Solutions...

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