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T T T T F F F F 1. If P, then Q is logically equivalent to If ~Q, then ~P. 2. The statement P→ Q is the converse of Q→ P. 3. The negation of P→Q is P→~Q. 4. The statement P→Q is equivalent to ~P ^ Q.

T T T T F F F F 1. If P, then Q is logically equivalent to If ~Q, then ~P. 2. The statement P→ Q is the converse of Q→ P. 3. The negation of P→Q is P→~Q. 4. The statement P→Q is equivalent to ~P ^ Q.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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Question
**Logic Statements and Their Equivalents** 1. **True**: If P, then Q is logically equivalent to If ~Q, then ~P. - This is known as the contrapositive. A statement is always logically equivalent to its contrapositive. 2. **False**: The statement P → Q is the converse of Q → P. - The converse of P → Q is Q → P, but it is not logically equivalent to P → Q. They are different statements and do not have the same truth values in all situations. 3. **False**: The negation of P → Q is P → ~Q. - The correct negation of P → Q is P ∧ ~Q, meaning P is true and Q is false. 4. **False**: The statement P → Q is equivalent to ~P ∧ Q. - This is incorrect. P → Q is equivalent to ~P ∨ Q, meaning either P is false or Q is true (or both). These logical equivalences are fundamental in understanding logical statements and their transformations.
Transcribed Image Text:**Logic Statements and Their Equivalents** 1. **True**: If P, then Q is logically equivalent to If ~Q, then ~P. - This is known as the contrapositive. A statement is always logically equivalent to its contrapositive. 2. **False**: The statement P → Q is the converse of Q → P. - The converse of P → Q is Q → P, but it is not logically equivalent to P → Q. They are different statements and do not have the same truth values in all situations. 3. **False**: The negation of P → Q is P → ~Q. - The correct negation of P → Q is P ∧ ~Q, meaning P is true and Q is false. 4. **False**: The statement P → Q is equivalent to ~P ∧ Q. - This is incorrect. P → Q is equivalent to ~P ∨ Q, meaning either P is false or Q is true (or both). These logical equivalences are fundamental in understanding logical statements and their transformations.
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