MAS111_09_assignment_03 - (1) p ∨ ( p ∧ q ) and p , (2)...

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NANYANG TECHNOLOGICAL UNIVERSITY MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 3 TUTORIALS: 07, 08, 09/09/09 1. Construct truth-tables for the following compound propositions: (1) ( p ∧ ¬ q ) ( p q ), (2) ( p q ) ( q p ), (3) ( p q ) ↔ ¬ r , 2. Construct truth-tables for the following compound propositions, and determine whether these propositions are tautology, contradiction or contingent. (1) ¬ p ( p q ), (2) (( p q ) q ) p , (3) ( p q ) ∨ ¬ ( p ∨ ¬ q ). 3. Establish the logical equivalence of the following compound proposi- tions, by constructing truth-tables:
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Unformatted text preview: (1) p ∨ ( p ∧ q ) and p , (2) p ∧ ( p ∨ q ) and p . 4. Use the standard logical equivalence given in the lecture, rather than truth-tables, to demonstrate that ( p → q ) ∧ ( p → ¬ q ) is logically equivalent to ¬ p . 5. Use the standard logical equivalence given in the lecture, rather than truth-tables, to demonstrate that ( p → ( q → r )) → (( p → q ) → ( p → r )) is a tautology....
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