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1. translate the following predicate expressions into English. The DoD

CS318, Spring 2019 Homework 2 e the following predicate expressions into English. The DoD is R. (2) Meanings of the predicates are: x is greater than y x-y z -(x, y. z etc. b) Vx 3y (x, y, 1) c) Vx Vy Vz+(x, y,z) d) 3xVy"(y, x, y) "(y, z, x) Translate the following English expressions into predicate logic. The DoD is the set of all oDU students. Create appropriate predicates as needed. (2) 2. a) Every student in CS381 will leam logic. b) At least one student is enrolled in CS381 and is not a CS major. c) Students who graduate with a CS major have all taken CS381. d) All students in CS381 have taken CS150 or CS333. 3. Name the rule of inference or equivalence that is being applied in each case. (2) b) -p 4. Complete this proof of the following propositional logic theorem. (2) Given: p v (q vn, p Prove: rvs r,qr) Given 2. p r 5. Which type of proof is being used in each case to prove the theorem "given A, prove C 7 (2) First Line Last Line Proof Type a