Problem Set 2 Predicates and Quantifiers (30 pts) (a) Let F(x) denote " x is my friend," and P(x) denote " x is perfect. What is the logical translation of the statement "All of my friends are perfect." (5 pts) (b) Let domain = fleegles, snurds, thingamabobs, predicates F(x):x is a feegle, S(x) : x is a snurd, and T(x):x is a thingamabob. Translate the following English sentences to predicate logic. (9 pts) (1) "Some fleegles are thingamabobs." (2) "All fleegles are snurds." (3) "No snurd is a thingamabob." (c) Let p(x,y) be the predicate " x+y is even", where x and y range over the integers. (16 pts) (1) Prove that xyp(x,y) is true. (2) Prove that yxp(x,y) is false