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Name: SSN: Grade:MA334 EXAM 1 February 1999I 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 Σ = {0, 1} be an alphabet. Let L1be the language consisting of all strings over Σ of length 4 inwhich the first symbol is a zero, and let L2be the language consisting of all strings over Σ of length4 in which the last symbol is a 0. Find1. L1− L22. L1∩ L23. L1∪ L23 (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,thenA ∩ Bc= ∅.2. (A ∪ B) xC⊆ (AxC) ∩ (BxC).3. A ∪ (B ∩ C) ⊆ (A ∪ B) ∩ (A ∪ C).4. (20pts)Prove that if n2is 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


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STEVENS MA 334B - MA 334 Exam 1

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