STEVENS MA 334B - MA 334 Exam 1 (5 pages)

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MA 334 Exam 1

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MA 334 Exam 1

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Pages:
5
School:
Stevens Institute of Technology
Course:
Ma 334b - Discrete Mathematics
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Name MA334 SSN EXAM 1 Grade February 1999 I pledge my honor that I have abided by the Stevens Honor System 1 10pts Let U Z Are the following true or false If false explain 1 x y x y y x 2 y x x y y x 2 15pts Let 0 1 be an alphabet Let L1 be the language consisting of all strings over of length 4 in which the first symbol is a zero and let L2 be the language consisting of all strings over of length 4 in which the last symbol is a 0 Find 1 L1 L2 2 L1 L2 3 L1 L2 3 20pts Let A B C be sets Do 2 of the 3 problems below Prove using the element method or disprove by a exhibiting a counterexample Note There is no such thing as Proof by Venn Diagram 1 If A B then A B c 2 A B x C A x C B x C 3 A B C A B A C 4 20pts Prove that if n2 is divisible by 3 then n is divisible by 3 Hint Consider the contrapositive 5 15pts Use a truth table to check the validity of the argument below P1 If I fail all the exams I ll fail the class P2 If I bring gifts to my TA I ll pass the class P3 I passed the class C I brought gifts to my TA 6 20pts Let A a b c and B 0 1 1 Define A relation from A to B 2 Define A function from A to B 3 Give an example of a function from A to B whose range does not equal its codomain 4 Give two examples of relations from A to B that are not functions 5 Find P A the power set of A

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