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MATH/COMP 61-02: Discrete Mathematics Tufts University Prof. Lenore Cowen Spring 2016 HW 2: due Thursday, February 4 Part I: From Richmond and Richmond do problems: • Section 1.4 (pp. 32-34): 3abcd, 7ab, 12, 13. • Section 1.6 (pp. 46-47): 1, 2ad, 5ab, 6abc, 7. Part II: You’ve had a bunch of problems where, given a logical formula, you can write down the truth table. How about the reverse? That is, if I give you a truth table, can you always come up with a formula that would give you exactly that truth table? How might you do that? Part III: A set S of logical connectives is called universal if for any statement using all the connectives we know (i.e. { ¬, ∨, ∧, →, ↔, }) there is a logically equivalent statement using only the connectives in S. 1. Prove or disprove: The set {¬, ∨, ∧} is universal 2. Prove or disprove: The set {¬, ∨} is universal