1 English to Predicate Logic Convert the following givens into formal predicate logic. Use the predicates given, you may not need all of them Then, negate the predicate sentence. Push all negations to the closest terms a) There is a fried vegetable that is not healthy. Let the domain of discourse be all food. - F(x) : True if x is fried - V(x) : True if x is a vegetable - H(x) : True if x is healthy b) Every programmer has more than one project. Let the domain of discourse be all people and projects. - Prog(x) : True if x is a programmer - Proj(x,y) : True if y is a project that x has - E(x,y) : True if x is the same as y Use laws of equivalence and inference rules to show how you can derive the conclusions from the given premises. Not all givens may be necessary Be sure to cite the rule and line number(s) used at each step. a) Givens 1pr2pq3q b) You may find addition and DeMorgan's laws to be especially helpful Givens 1pq2q(sr)3sr Inference Rules