# Past Exam for CMSC 250 - Discrete Structures with Perlis at Maryland (UMD)

## Exam Information

 Material Type: Practice Exam 1 Professor: Perlis Class: CMSC 250 - Discrete Structures Subject: Computer Science University: University of Maryland Term: Fall 2008 Keywords: Either...orContradictionConjunctionGeneralizationConditionalInfinite SetsPractice ExamPropositionalEliminationTransitivity

## Sample Document Text

250, practice exam-I 1. Is q ceilingleft2ceilingright < l ? 2 m ? EXPLAIN. 2. What is P4i=1ceilingleft(i+10)/(i+1)ceilingright? (note- each term has a ceiling.) 3. For each of the following arguments, either (1) write valid and show it is valid using only the rules of logic on the sheet (which are at the back of the exam), or (2) Write not valid and show why using rows of a truth table. (a) p1 : p1 ? p2 p2 : p2 ? p3 p3 : p3 ? p4 p4 : p4 ? p5 p5 : p5 ? p6 p6 : p6 ? p7 p7 : p7 ? p1 conclusion : p2 ? p1 (b) p1 : p1 ?p2 ?¬p3 p2 : ¬p1 ?p3 p3 : p3 ? p1 conclusion ¬p1 ?¬p2 4. For this problem the symbols ?, ?, and || (the absolute value sign) have their usual meaning. for the sentence below, give (1) a non-empty domain where the sentence is true, and (2) a non-empty domain where the sentence is false. all domains given should be subsets of r (the reals). Justify your answers (one brief sentence each). (?z)(?x)(?y)[|x?y|? z]. 5. Prove the following. (a) for all naturals x, if x5 ? 0 (...

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