Math.3336 Homework Assignment 3

Due Thursday, 02/07, 11:59pm

1. Consider the following hypotheses:

H1 : x (p(x) q(x)) H2 : x (q(x) r(x)) Use rules of inference to prove that the following conclusion follows from these hypotheses:

C : x (p(x) r(x)) Clearly label the inference rules used at every step of your proof.

2. Consider the following hypotheses:

H1 : x (C(x) A(x)) H2 : x (A(x) y B(y)) H3 : x A(x) Use rules of inference to prove that the following conclusion follows from these hypotheses:

C : x (B(x) C(x)) Clearly label the inference rules used at every step of your proof.

3.

Consider the following predicate quantified formula:

x y (P (x, y) P (y, y)) Prove the unsatisability of this formula using rules of inference.

1 4. Translate into English the statement