1 English to Predicate Logic Convert the following givens into formal predicate logic, Use the predicates given, you mag not need all of them Then, negate the predicate sentence. Push all negations to the closest rerms - F(x) : 'lyue if x is friod - V(x) True if x is a vegetable - H(x) : True if x is healthy b) Etery proyrammer has mare than one project. Let the domain of disoourse be all people and projocts. - Prog(x): True if x is a programrer - Proj(x.y): True if y is a projert that x has - F. (x,y): True if x is the same as y 2 Inference proofs Use luns of equivalenee and iaference rules tu show hem you car derive the canchnsions from the given premiss. Not all givens may be necessary Be sure tw cile the rule amb line number(s) used at coch step. a) Givens 1pr2pq3q b) You nay fised addiqur and DeWoryan's has lo de: esperaingy helpjul (Hiven: 1p42q>(SA)3r