# Past Exam for MATH 2534 - Intro Discrete Math at Virginia Tech (VT)

## Exam Information

 Material Type: Exam 1 Professor: Staff Class: MATH 2534 - Intro Discrete Math Subject: Mathematics University: Virginia Polytechnic Institute And State University Term: Spring 2008 Keywords: ContrapositiveSpring 2008 ProblemContradictionFollowing ProblemFalse StatementPropositionalFollowing StatementsValid ArgumentPrime NumberMathematics

## Sample Document Text

Math 2534 Test 1 Solutions Spring 2008 Problem 1: (8pts) Given the following statements: p: Mary is a Math major q: James is a CS major r: Karla is an Engineer w: Harry is a Hokie Given the statement: ()()p qrw¬?¬ ? ? is false and p is false, determine if r, p, q, and w are true or false and justify your reasoning. Solutions: We know the implication ( ) ( )p qrw¬ ?¬ ? ? is false and p is also false. We also know that ( )p q¬?¬ must be true and ( )rw? must be false in order for the implication to be false. Since the "or" statement ( )p q¬ ?¬ is true and p is false, then we know that is true but and q can not be derermined. pq¬¬ Since ( )rw? is false and is an "or" statement then r and w are both false. Problem 2: (8pts) Express the following sentences in symbolic logic using multiple quantifiers. Specify domains for each variable used and define a predicate P(x,y) a) Most people like some fast food restaurants. b) Each of us has a favorit...

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