HW 1 - MATH 290 – HOMEWORK 1 – SOLUTIONS 1. Show the...

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Unformatted text preview: MATH 290 – HOMEWORK 1 – SOLUTIONS 1. Show the following using a truth table. (a) ( P ∧ Q ) = ⇒ R is equivalent to ( P = ⇒ R ) ∨ ( Q = ⇒ R ) (b) P = ⇒ ( Q ∨ R ) is equivalent to ( P ∧ ∼ Q ) = ⇒ R ). Solution: (a). P Q R P ∧ Q P = ⇒ R Q = ⇒ R P ∧ Q = ⇒ R ( P = ⇒ R ) ∨ ( Q = ⇒ R ) T T T T T T T T T T F T F F F F T F T F T T T T T F F F F T T T F T T F T T T T F T F F T F T T F F T F T T T T F F F F T T T T (b). P Q R Q ∨ R P ∧ ∼ Q P = ⇒ ( Q ∨ R ) P ∧ ∼ Q = ⇒ R T T T T F T T T T F T F T T T F T T T T T T F F F T F F F T T T F T T F T F T F T T F F T T F T T F F F F F T T 2. Consider the following sentence taken from Form 1040, “ If you file a complete and accurate tax return and you are due a refund, your refund will be issued within 40 days if you file a paper return or within 21 days if you file electronically. ” (a) Write the above statement as a propositional form clearly defining simple, relevant propositions by the letters P , Q , R , etc. For example, you might say “Let P = ‘you filed a complete tax return’, and Q = ‘you filed an accurate tax return.’ ” etc....
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This note was uploaded on 03/05/2011 for the course MATH 290 taught by Professor Alligood,k during the Fall '08 term at George Mason.

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HW 1 - MATH 290 – HOMEWORK 1 – SOLUTIONS 1. Show the...

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