Explanation Given: The given argument is, No professor is uneducated. No monkey is educated. Therefore, no professor is a monkey. Description: 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, No professor is uneducated. No monkey is educated. Therefore, no professor is a monkey. p : A person is a professor. q : A person is educated. r : An animal is a monkey. Premise 1 is “No professor is uneducated.” that can be rephrased as “If a person is a professor, he is educated.” The symbolic form of premise 1 is p → q . Premise 2 is “No monkey is educated.” that can be rephrased as “If he is a monkey, he is not educated.” The symbolic form of premise 2 is r → ∼ q . Conclusion is “Therefore, no professor is a monkey.” that can be rephrased as “If a person is a professor, he is not a monkey.” The symbolic form of conclusion is p → ∼ r . The symbolic form of the given argument is, p → q r → ∼ q _ p → ∼ r The given argument is represented by the conditional [ ( p → q ) ∧ ( r → ∼ q ) ] → ( p → ∼ r )

MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

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ISBN: 9780357537343

Author: Johnson

Publisher: CENGAGE L

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The validity of the given argument by using truth table.

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