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rec0517_key

rec0517_key - COT 3100 Summer 2001 Recitation 05/17 Logic 1...

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Unformatted text preview: COT 3100 Summer 2001 Recitation 05/17 Logic 1. Use truth tables to determine which of the following formulas are equivalent to each other: a) ( p ∧ q ) ∨ ( ¬ p ∧¬ q ) b) ¬ p ∨ q c) ( p ∨¬ q ) ∧ ( q ∨¬ p ) d) ¬ ( p ∨ q ) e) ( q ∧ p ) ∨¬ p a) is equivalent to c) b) is equivalent to e) 2. Let p & q be a binary operator NOR, that means neither p nor q . a) Make a truth table for p & q p q p & q 1 1 1 1 1 b) Find a formula using only the connectives ∧ , ∨ , and ¬ that is equivalent to p & q . p & q = ¬ ( p ∨ q )=( ¬ p ) ∧ ( ¬ q ) c) Find formulas using only the connective & that are equivalent to ¬ p , p ∨ q , and p ∧ q . ¬ p = p & p p ∨ q = ¬ ( p & q )=( p & q )& ( p & q ) p ∧ q = ( ¬ p )&( ¬ q )=( p & p )&( q & q ) 3. Use laws of logic to simplify the following formulas: a) ¬ ( ¬ p ∧¬ q ) ¬ ( ¬ p ∧¬ q )= p ∨ q b) ¬ ( ¬ p ∨ q ) ∨ ( p ∧¬ r ) ¬ ( ¬ p ∨ q ) ∨ ( p ∧¬ r )=( p ∧¬ q ) ∨ ( p ∧¬ r )= p ∧ (( ¬...
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