Logic Strand Lecture 3

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Exercises: • Determine if the following statements are logically equivalent. P :~ ( p ∨ q), Q :~ p∧ ~ q p q ~( p ∨ q) ~p ∧ ~q Step: • Determine if ~ ( p ∧ q) ⇔~ p∨ ~ q is a tautology, and hence if ~ ( p ∧ q) ≡~ p∨ ~ q . p q ~( p ∧ q) ⇔ ~p ∨ ~q Step: WUCT121 <strong>Logic</strong> 52
1.6.2. Substitution There are two different types of substitution into statements. Rule of Substitution: If in a tautology all occurrences of a variable are replaced by a statement, the result is still a tautology. Examples: • We know P ∨ ~ P is a tautology. Thus, by the rule of substitution, so too are: ∗ Q ∨ ~ Q, by letting Q = P. ∗ (( p ∧ q) ⇒ r) ∨ ~ (( p ∧ q) ⇒ r) , by letting ( p ∧ q) ⇒ r = P . Note: We have simply replaced every occurrence of P in the tautology P ∨ ~ P , by some other statement. WUCT121 <strong>Logic</strong> 53
Page 1 and 2: 1.5.2. Contradiction Definition: Co
Page 3 and 4: 1.5.2.1 Quick Method for Showing a
Page 5 and 6: Exercise: • Use the “quick” m
Page 7 and 8: Exercises: • Complete the truth t
Page 9: Examples: • Determine if the foll
Page 13 and 14: 1.6.3. Laws The following logical e
Page 15 and 16: Example: Prove the first of De Morg
Page 17: • ( p ⇒ q) ≡ ( ~ q ⇒~ p)

Logic Strand Lecture 3

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