Let P(x, y) be a binary predicate where the type of x is A and the...

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Πι 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 ₁ (P) to be the unary predicate on A defined as follows: T₁ (P)(x) is true if and only if there exists an element y of B such that P(x, y) is true. Similarly, 72(P) is the unary predicate on B defined so that 72(P)(y) is true if and only if there exists an element x of A such that P(x, y) is true. B = (a) Let A {0, 1, 2, 3} and define P(x, y) to mean “x < y”. Describe T₁ (P) and T2(P) as both predicates and relations. (b) What can you say about the predicate P if you know that π₁(P) and 2 (P) are each always false? What if they are each always true? Πι 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 ₁ (P) to be the unary predicate on A defined as follows: T₁ (P)(x) is true if and only if there exists an element y of B such that P(x, y) is true. Similarly, 72(P) is the unary predicate on B defined so that 72(P)(y) is true if and only if there exists an element x of A such that P(x, y) is true. B = (a) Let A {0, 1, 2, 3} and define P(x, y) to mean “x < y”. Describe T₁ (P) and T2(P) as both predicates and relations. (b) What can you say about the predicate P if you know that π₁(P) and 2 (P) are each always false? What if they are each always true?

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The question asks What can you say about the predicate P if you know that P and P are each always false What if they are each always true Understanding the notation Px y is a binary predicate which me... View the full answer