Logic Strand Lecture 3
Logic Strand Lecture 3
Logic Strand Lecture 3
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1.6. <strong>Logic</strong>al Equivalence<br />
Definition: <strong>Logic</strong>al Equivalence.<br />
Two statements are logically equivalent if, and only if, they<br />
have identical truth values for each possible substitution of<br />
statements for their statements variables.<br />
The logical equivalence of two statements P and Q is<br />
denoted<br />
P ≡ Q.<br />
If two statements P and Q are logically equivalent then<br />
P ⇔ Q is a tautology<br />
1.6.1. Determining <strong>Logic</strong>al Equivalence.<br />
To determine if two statements P and Q are logically<br />
equivalent, construct a full truth table for each statement. If<br />
their truth values at the main connective are identical, the<br />
statements are equivalent.<br />
Alternatively show<br />
conclude<br />
P ≡ Q.<br />
P ⇔ Q is a tautology and hence<br />
WUCT121 <strong>Logic</strong> 50
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