Explanation Given: The given argument is, If the defendant is guilty, he goes to jail. The defendant does not go to jail. Therefore, the defendant is not guilty. Description: The disjunction p ∨ q joins the two statements with the word “or”. 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 p ∧ q joins the two statements with the word “and”. 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. The conditional statement p → q is made up of two statements p and q . It follows the form “If p , then q ”. 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 false 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. Approach: In the given statement, If the defendant is guilty, he goes to jail. The defendant does not go to jail. Therefore, the defendant is not guilty. p : The defendant is guilty. q : The defendant goes to jail. Premise 1 is “If the defendant is guilty, he goes to jail.” The symbolic form of premise 1 is p → q . Premise 2 is “The defendant does not go to jail.” The symbolic form of premise 2 is ∼ q . Conclusion is “Therefore, the defendant is not guilty.” The symbolic form of conclusion is ∼ p . The symbolic form of the given argument is, p → q ∼ q _ ∼ p The given argument is represented by the conditional [ ( p → q ) ∧ ( ∼ q ) ] → ( ∼ p )

8th Edition

ISBN: 9780357425831

Author: Johnson

Publisher: CENGAGE L

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Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities.…

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Chapter 1.CR, Problem 58CR

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The validity of the given argument by using truth table.

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