Explanation Given: The given argument is, If George prepares gourmet food, then he is a good cook. If Brenda does not prepare gourmet food, then Sarah buys fast food. Sarah does not buy fast food. Therefore, George does not prepare gourmet food, and Brenda does not prepare gourmet food. Approach: The meaning of the logical connectives symbols are as follows, Name Logical Connective Symbol Conjunction and ∧ Disjunction or ∨ Negation not ∼ Conditional If…then → Bi-conditional If and only if ↔ Table ( 1 ) The disjunction is true if at least one of the components of the disjunction is true. The disjunction is false if both the statements are false. The conjunction is true if both the components of the conjunction is true. The conjunction is false if at least one of the statements is false. If the statement p is true, the conditional statement will depend on whether the statement q is true or false. If the statement p is false, the conditional statement will be true and does not depend on whether the statement q is true or false. The negation ∼ p is the opposite of the statement p . If the component of the statement is true, the negation of statement is false and vice-versa. An argument having n premises P 1 , P 2 , P 3 , ... , P n and conclusion C can be represented by the conditional [ P 1 ∧ P 2 ∧ P 3 ∧ ... ∧ P n ] → C . An argument is valid if and only if the conditional [ P 1 ∧ P 2 ∧ P 3 ∧ ... ∧ P n ] → C is a tautology. Calculation: Consider the statements as follows: p : George prepare gourmet food. q : George is a good cook. r : Brenda does not prepare gourmet food. s : Sarah buys fast food. The symbolic form of the argument is, p → q r → s ∼ s _ ∴ ∼ p ∧ r Therefore, the conditional for the argument is, [ ( p → q ) ∧ ( r → s ) ∧ ∼ s ] → ( ∼ p ∧ r ) There are 4 letters in the given symbolic expression. So, there will be 2 4 = 16 rows in the truth table. One column for p , second column for q , third column for r , fourth column for s , fifth column for ~ p , sixth column for ∼ s , seventh column for p → q , eighth column for r → s , ninth column for ∼ p ∧ r , tenth column for [ ( p → q ) ∧ ( r → s ) ∧ ~ s ] , and eleventh column for the conditional statement [ ( p → q ) ∧ ( r → s ) ∧ ∼ s ] → ( ∼ p ∧ r )

11th Edition

ISBN: 9781337496094

Author: Tan

Publisher: CENGAGE C

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Logic and Proofs

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Chapter A.5, Problem 23E

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Ch. A.1 - In Exercises 114, determine whether the statement...Ch. A.1 - Prob. 2E Ch. A.1 - Prob. 3E Ch. A.1 - Prob. 4E Ch. A.1 - Prob. 5E Ch. A.1 - Prob. 6E Ch. A.1 - Prob. 7E Ch. A.1 - Prob. 8E Ch. A.1 - Prob. 9E Ch. A.1 - Prob. 10E

Ch. A.1 - Prob. 11E Ch. A.1 - Prob. 12E Ch. A.1 - Prob. 13E Ch. A.1 - Prob. 14E Ch. A.1 - Prob. 15E Ch. A.1 - Prob. 16E Ch. A.1 - Prob. 17E Ch. A.1 - Prob. 18E Ch. A.1 - Prob. 19E Ch. A.1 - Prob. 20E Ch. A.1 - Prob. 21E Ch. A.1 - Prob. 22E Ch. A.1 - Prob. 23E Ch. A.1 - Prob. 24E Ch. A.1 - Prob. 25E Ch. A.1 - Prob. 26E Ch. A.1 - Prob. 27E Ch. A.1 - Prob. 28E Ch. A.1 - Prob. 29E Ch. A.1 - Let p and q denote the propositions p: The...Ch. A.1 - Prob. 31E Ch. A.1 - Prob. 32E Ch. A.1 - Prob. 33E Ch. A.2 - Prob. 1E Ch. A.2 - Prob. 2E Ch. A.2 - Prob. 3E Ch. A.2 - Prob. 4E Ch. A.2 - In Exercises 1-18, construct a truth table for...Ch. A.2 - Prob. 6E Ch. A.2 - Prob. 7E Ch. A.2 - In Exercises 1-18, construct a truth table for...Ch. A.2 - Prob. 9E Ch. A.2 - Prob. 10E Ch. A.2 - Prob. 11E Ch. A.2 - Prob. 12E Ch. A.2 - Prob. 13E Ch. A.2 - Prob. 14E Ch. A.2 - Prob. 15E Ch. A.2 - Prob. 16E Ch. A.2 - Prob. 17E Ch. A.2 - Prob. 18E Ch. A.2 - If a compound proposition consists of the prime...Ch. A.3 - In Exercises 14, write the converse, the...Ch. A.3 - In Exercises 14, write the converse, the...Ch. A.3 - Prob. 3E Ch. A.3 - Prob. 4E Ch. A.3 - Prob. 5E Ch. A.3 - In Exercises 5 and 6, refer to the following...Ch. A.3 - Prob. 7E Ch. A.3 - Prob. 8E Ch. A.3 - Prob. 9E Ch. A.3 - Prob. 10E Ch. A.3 - Prob. 11E Ch. A.3 - Prob. 12E Ch. A.3 - Prob. 13E Ch. A.3 - Prob. 14E Ch. A.3 - Prob. 15E Ch. A.3 - Prob. 16E Ch. A.3 - Prob. 17E Ch. A.3 - Prob. 18E Ch. A.3 - Prob. 19E Ch. A.3 - Prob. 20E Ch. A.3 - Prob. 21E Ch. A.3 - Prob. 22E Ch. A.3 - Prob. 23E Ch. A.3 - Prob. 24E Ch. A.3 - Prob. 25E Ch. A.3 - Prob. 26E Ch. A.3 - Prob. 27E Ch. A.3 - Prob. 28E Ch. A.3 - Prob. 29E Ch. A.3 - Prob. 30E Ch. A.3 - Prob. 31E Ch. A.3 - Prob. 32E Ch. A.3 - Prob. 33E Ch. A.3 - Prob. 34E Ch. A.3 - Prob. 35E Ch. A.3 - Prob. 36E Ch. A.3 - Prob. 37E Ch. A.3 - Prob. 38E Ch. A.4 - Prove the idempotent law for conjunction, ppp.Ch. A.4 - Prob. 2E Ch. A.4 - Prove the associative law for conjunction,...Ch. A.4 - Prob. 4E Ch. A.4 - Prove the commutative law for conjunction, pqqp.Ch. A.4 - Prob. 6E Ch. A.4 - Prob. 7E Ch. A.4 - Prob. 8E Ch. A.4 - Prob. 9E Ch. A.4 - Prob. 10E Ch. A.4 - Prob. 11E Ch. A.4 - Prob. 12E Ch. A.4 - Prob. 13E Ch. A.4 - Prob. 14E Ch. A.4 - Prob. 15E Ch. A.4 - Prob. 16E Ch. A.4 - Prob. 17E Ch. A.4 - In exercises 9-18, determine whether the statement...Ch. A.4 - Prob. 19E Ch. A.4 - Prob. 20E Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - Prob. 22E Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - Prob. 26E Ch. A.5 - Prob. 1E Ch. A.5 - Prob. 2E Ch. A.5 - Prob. 3E Ch. A.5 - Prob. 4E Ch. A.5 - Prob. 5E Ch. A.5 - Prob. 6E Ch. A.5 - Prob. 7E Ch. A.5 - Prob. 8E Ch. A.5 - Prob. 9E Ch. A.5 - In Exercises 116, determine whether the argument...Ch. A.5 - Prob. 11E Ch. A.5 - Prob. 12E Ch. A.5 - Prob. 13E Ch. A.5 - Prob. 14E Ch. A.5 - Prob. 15E Ch. A.5 - Prob. 16E Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - Prob. 18E Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - Prob. 22E Ch. A.5 - Prob. 23E Ch. A.5 - Prob. 24E Ch. A.5 - Prob. 25E Ch. A.6 - In Exercises 1-5, find a logic statement...Ch. A.6 - Prob. 2E Ch. A.6 - Prob. 3E Ch. A.6 - Prob. 4E Ch. A.6 - Prob. 5E Ch. A.6 - Prob. 6E Ch. A.6 - Prob. 7E Ch. A.6 - Prob. 8E Ch. A.6 - Prob. 9E Ch. A.6 - Prob. 10E Ch. A.6 - Prob. 11E Ch. A.6 - Prob. 12E Ch. A.6 - Prob. 13E Ch. A.6 - In Exercise 12-15, find a logic statement...Ch. A.6 - Prob. 15E Ch. A.6 - Prob. 16E

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The given argument is valid.

Solution Summary: The author explains the meaning of the logical connectives symbols, which are as follows: Name Logical Connective Symbol Conjunction and wedge

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The given argument is valid.