Let P(x, y) be a binary predicate where the type of x is A and the type of y is B. We define the projection π1(P) to be the unary predicate on A defined as follows: π1(P)(x) is true if and only if there exists an element y of B such that P(x, y) is true. Similarly, π2(P) is the unary predicate on B defined so that π2(P)(y) is true if and only if there exists an element x of A such that P(x, y) is true. (a) Let A = B = {0, 1, 2, 3} and define P(z, y) to mean "x < y". Describe π1 (P) and π2(P) as both predicates and relations
(b) What can you say about the predicate P if you know that Ti(P) and m(P) are each always false? What if they are each always true?
(c) (uses Java) Suppose you are given a boolean method isInP(int x, int y) where each of z and y are restricted to the range from 0 through LENCTH 1. Write boolean methods that will return the value of the predicates π1(P) and 7T2(P), given appropriate input.