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Exploring Validity of Logical Arguments through Symbolic Formulation

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This quiz focuses on methods of proof and the validation of logical arguments. Participants are asked to identify two rules of inference through their equations and the respective tautologies they are based on. Additionally, three arguments concerning studying hard, getting A’s, and financial success are to be formulated symbolically. The validity of each argument will be assessed using logical reasoning, determining whether conclusions drawn are valid based on the given premises.

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Exploring Validity of Logical Arguments through Symbolic Formulation

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  1. Quiz 6 1.5 Methods of Proof.

  2. Quiz 5: Th. May 26 3.30-3.45 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.

  3. 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. pq 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 pq If I don’t get rich then I don’t get A’s NOT r  NOT q  qr Therefore: I get rich r (this is wrong because we don’t know if p=T, we may only conclude pr). 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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