MAS111_09_assignment_03-hints

MAS111_09_assignment_03-hints - NANYANG TECHNOLOGICAL...

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NANYANG TECHNOLOGICAL UNIVERSITY MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 3 HINTS 1. Construct truth-tables for the following compound propositions: (1) ( p ∧¬ q ) ( p q ), (2) ( p q ) ( q p ), (3) ( p q ) ↔ ¬ r , Hint : Truth-table construction. 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 ). Hint : Truth-table construction. Contingents. 3. Establish the logical equivalence of the following compound proposi- tions, by constructing truth-tables: (1) p ( p q ) and p , (2) p ( p q ) and p . Hint : Truth-table construction. 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 .
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Hint : ( p q ) ( p → ¬ q ) ( ¬ p q
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MAS111_09_assignment_03-hints - NANYANG TECHNOLOGICAL...

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