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Quiz 6 1.5 Methods of Proof.

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Quiz 5: Th. May pm 1) Give 2 rules of inference (no names, just the equations) and the tautologies on which they are based. 2) Formulate the following arguments symbolically and determine whether each one is valid: (p=“I study hard”, q=“I get A’s”, r=“I get rich”) a) If I study hard then I get A’s. I did not study hard. Therefore: I will not get A’s. b) If I study hard then I get A’s If I don’t get rich then I don’t get A’s Therefore: I get rich c) If I study hard then I get A’s or I get rich I don’t get A’s and I don’t get rich Therefore: I don’t study hard.

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Answers Quiz 5 1) Give 2 rules of inference (no names, just the equations) and the tautologies on which they are based. book page 58 table 1. 2) Formulate the following arguments symbolically and determine whether each one is valid: (p=“I study hard”, q=“I get A’s”, r=“I get rich”) a) If I study hard then I get A’s. pq I did not study hard. NOT p Therefore: I will not get A’s. NOT q (invalid). b) If I study hard then I get A’s pq If I don’t get rich then I don’t get A’s NOT r NOT q qr Therefore: I get rich r (this is wrong because we don’t know if p=T, we may only conclude pr). c) If I study hard then I get A’s or I get rich p (q OR r) (NOT q) AND (NOT r) NOT p I don’t get A’s and I don’t get rich (NOT q) AND (NOT r) Therefore: I don’t study hard. NOT p (yes this is correct).

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