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# Use rules of inference lo show that if the premises and ISBN: 9780073383095 37

## Solution for problem 37E Chapter 1.SE

Discrete Mathematics and Its Applications | 7th Edition

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Problem 37E

Use rules of inference lo show that if the premises and ¬R(a), where a is in the domain, are true, then the conclusion ¬P(a) is true.

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Solution:Step1: In this problem, we have to use rules of inference to show that if the premises and ¬R(a), where a is in the domain, are true, then the conclusion ¬P(a) is true.Step 2: For this condition, we can use the combining rules of inference for Propositions and Quantified statement Universal Modus Ponens: ) P(a), where a is a specific element in the given domain Therefore, Q(a) is true Universal Modus Tollens: )Q(a), where a is a specific element in the given domain Therefore, P(a) is true Take an example: The premises:”Every man has two hands.” “Eddy is a man”Let P(x) denote “x is a man” and Q(x) denote “x has two hands” and Eddy in the member of the domain.Valid Argument: )Similarly In the given problem we have ) means P(a) (by Universal Modus Tollens)Therefore , Q(a) is true

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##### ISBN: 9780073383095

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