Explanation Given: The given statements are, i. If you answer yes to all of the above, then you complete Part II. ii. If you answer no to any of the above, then you do not complete Part II. iii. If you completed Part II, then you answered yes to all of the above. iv. If you did not complete Part II, then you answered no to at least one of the above. Definition: The statements are said to be equivalent if the respective truth table of the statement are identical for the corresponding entries. The conditional ( p → q ) are of three variations: Variation Symbolic form Read as The converse q → p If q then p The inverse ∼ p → ∼ q If not p then q The contrapositive ∼ q → ∼ p If not q then p Approach: The given statements are, i. If you answer yes to all of the above, then you complete Part II. ii. If you answer no to any of the above, then you do not complete Part II. iii. If you completed Part II, then you answered yes to all of the above. iv. If you did not complete Part II, then you answered no to at least one of the above. Consider, p : Answer yes to all of the above q : You complete Part II ∼ p : Answered no to at least one of the above ∼ q : You did not complete Part II The symbolic expression for given statements are, p → q : If you answer yes to all of the above, then you complete Part II. ∼ p → ∼ q : If you answer no to any of the above, then you do not complete Part II. q → p : If you completed Part II, then you answered yes to all of the above. ∼ q → ∼ p : If you did not complete Part II, then you answered no to at least one of the above

8th Edition

ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Chapter 1.4, Problem 52E

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The pair of equivalent statements from the given statements.

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Chapter 1.4, Problem 51E

Chapter 1.4, Problem 53E

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