Tutorial6_Intro_Logic

Tutorial6_Intro_Logic - COMP 170 Introduction to Logic...

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Unformatted text preview: COMP 170 Introduction to Logic & Quantifiers Tutorial Problem 1 Problem 1 Show that the statements s ⇒ t and ¬ s ∨ t are equivalent. Give the truth table for s ⇒ t and ¬ s ∨ t , and compare them. Problem 1 Show that the statements s ⇒ t and ¬ s ∨ t are equivalent. s t s ⇒ t ¬ s ∨ t T T T T T F F F F T T T F F T T Give the truth table for s ⇒ t and ¬ s ∨ t , and compare them. Problem 1 Show that the statements s ⇒ t and ¬ s ∨ t are equivalent. s t s ⇒ t ¬ s ∨ t T T T T T F F F F T T T F F T T Give the truth table for s ⇒ t and ¬ s ∨ t , and compare them. Problem 1 Show that the statements s ⇒ t and ¬ s ∨ t are equivalent. s t s ⇒ t ¬ s ∨ t T T T T T F F F F T T T F F T T Give the truth table for s ⇒ t and ¬ s ∨ t , and compare them. Problem 1 Show that the statements s ⇒ t and ¬ s ∨ t are equivalent. s t s ⇒ t ¬ s ∨ t T T T T T F F F F T T T F F T T Give the truth table for s ⇒ t and ¬ s ∨ t , and compare them. Problem 1 Show that the statements s ⇒ t and ¬ s ∨ t are equivalent. Show that p ⊕ q (the exclusive or of p and q ) is equivalent to ( p ∧ ¬ q ) ∨ ( ¬ p ∧ q ) . Problem 2 Show that p ⊕ q (the exclusive or of p and q ) is equivalent to ( p ∧ ¬ q ) ∨ ( ¬ p ∧ q ) . Problem 2 Use truth tables. Show that p ⊕ q (the exclusive or of p and q ) is equivalent to ( p ∧ ¬ q ) ∨ ( ¬ p ∧ q ) . p q p ⊕ q ¬ p ¬ q ) ( p ∧ ¬ q ) ∨ ( ¬ p ∧ q ) T T F F F F T F T F T T F T T T F T F F F T T F Problem 2 Use truth tables. Show that p ⊕ q (the exclusive or of p and q ) is equivalent to ( p ∧ ¬ q ) ∨ ( ¬ p ∧ q ) . p q p ⊕ q ¬ p ¬ q ) ( p ∧ ¬ q ) ∨ ( ¬ p ∧ q ) T T F F F F T F T F T T F T T T F T F F F T T F Problem 2 Use truth tables. (a) Is w ∧ ( u ⊕ v ) equivalent to ( w ∧ u ) ⊕ ( w ∧ v ) ? Problem 3 (Distributive “Laws”) (a) Is w ∧ ( u ⊕ v ) equivalent to ( w ∧ u ) ⊕ ( w ∧ v ) ? Problem 3 (Distributive “Laws”) Yes! ∧ distributes over ⊕ . Proof is below (a) Is w ∧ ( u ⊕ v ) equivalent to ( w ∧ u ) ⊕ ( w ∧ v ) ? Problem 3 (Distributive “Laws”) Yes! ∧ distributes over ⊕ . Proof is below Compare the truth tables of w ∧ ( u ⊕ v ) and ( w ∧ u ) ⊕ ( w ∧ v ) . (a) Is w ∧ ( u ⊕ v ) equivalent to ( w ∧ u ) ⊕ ( w ∧ v ) ? Problem 3 (Distributive “Laws”) Yes! ∧ distributes over ⊕ . Proof is below Compare the truth tables of w ∧ ( u ⊕ v ) and ( w ∧ u ) ⊕ ( w ∧ v ) . w u v w ∧ u w ∧ v ( w ∧ u ) ⊕ ( w ∧ v ) ( u ⊕ v ) w ∧ ( u ⊕ v ) T T T T T F F F T T F T F T T T T F T F T T T T T F F F F F F F F T T F F F F F F T F F F F T F F F T F F F T F F F F F F F F F (a) Is w ∧ ( u ⊕ v ) equivalent to ( w ∧ u ) ⊕ ( w ∧ v ) ?...
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Tutorial6_Intro_Logic - COMP 170 Introduction to Logic...

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