Logic Strand Lecture 3

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Exercises: • Complete the truth table for the statement ~ ( P ∨ Q) ∧ P to show it is a contradiction. P Q ~(P ∨ Q) ∧ P Step: • Complete the truth table for the statement ( P ∧ Q) ∧ ~ Q to show it is a contradiction. P Q (P ∧ Q) ∧ ~Q) Step: WUCT121 <strong>Logic</strong> 44
1.5.2.1 Quick Method for Showing a Contradiction The quick method for determining if a compound statement is a tautology can be used similarly for showing a contradiction. The quick method relies on the fact that if a truth value of “T” can occur under the main connective (for some combination of truth values for the components), then the statement is not a contradiction. If this truth value is not possible, then we have a contradiction. Therefore, to determine whether a statement is a contradiction, we place a “T” under the main connective and work backwards. WUCT121 <strong>Logic</strong> 45
Page 1: 1.5.2. Contradiction Definition: Co
Page 5 and 6: Exercise: • Use the “quick” m
Page 7 and 8: Exercises: • Complete the truth t
Page 9 and 10: Examples: • Determine if the foll
Page 11 and 12: 1.6.2. Substitution There are two d
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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