Exam s 1-4 Solutions

Exam s 1-4 Solutions - MATH 290 EXAM 1 SOLUTIONS Answer all...

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MATH 290 – EXAM 1 – SOLUTIONS Answer all of the following questions on the answer sheets provided. Show all work, as partial credit may be given. This test will be counted out of a total of 60 points. 1. (8 pts.) Prove that P = ( Q R ) is equivalent to ( P ∧ ∼ Q ) = R by ﬁlling in the truth table below. P Q R Q R P = ( Q R ) P ∧ ∼ Q ( P ∧ ∼ Q ) = R T T T T T F T T T F T T F T T F T T T T T T F F F F T F F T T T T F T F T F T T F T F F T T T F T F F F F T F T 2. (8 pts. each) Consider the statement: If a + b is even, then both a and b are even or both a and b are odd. (a) Translate the above statement into symbolic form. (b) Identify the antecedent and consequent of the statement. (c) State in English the converse of the statement. (d) State in English the contrapositive of the statement. Solution: (a) ( a + b even ) = ([( a even ) ( b even )] [( a odd ) ( b odd )]). (b) The antecedent of the above implication is (

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Exam s 1-4 Solutions - MATH 290 EXAM 1 SOLUTIONS Answer all...

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