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

## Exam Information

 Material Type: Exam Professor: McQuain Class: MATH 2534 - Intro Discrete Math Subject: Mathematics University: Virginia Polytechnic Institute And State University Term: Spring 2009 Keywords: ContrapositiveDirect MethodRational NumberContradictionDefinitionsValid ArgumentNecessary ConditionPropositionalPrime NumberNatural Numbers

## Sample Document Text

Math 2534 Test 1A Solutions Problem 1: Put the following statement into symbolic logic with multiple quantifiers. Each student at VT takes at least one math course. Solution: (8pts) Let S be the set of all students at VT Let M be the set of all math courses P(x,y): x take y ,(,)x SyMPxy?? ?? = ,( ) [ ( , )]x xS yyMPxy?????? Problem 2 If the operation of "nor" is defined to be p ? q ? ? (p ? q). Then use the algebra of logic to prove the following theorem and justify each step. Theorem: (p ? q) ? ( p ? q) ? p ? q. Solution: ( 12pts) Theorem: (p ? q) ? ( p ? q) ? p ? q. Proof: (p ? q) ? ( p ? q) = [ ( ) ( )] Definition of "nor" ( ) ( ) De Morgan's Law Idempotent pq pq pq pq pq ¬¬ ? ?¬ ? ? ???? ? Therefore (p ? q) ? ( p ? q) ? p ? q. Problem 3 Are the following two statements equivalent? Justify your answer using symbolic logic along with...

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