1. Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Qx): x is a perfect square Are the following logical expressions propositions? If the answer is yes, indicate wh ether the statement is true or false. (3 pts) a. P(x) b. P(2) 2. Consider the fllowing statements in English. Write a logical expression with the same meaning The domain of discourse must be the set of all real numbers. (4 pts) a. There is a number whose cube is equal to -2 b. The reciprocal ofevery number between 0 and 1 is greater than 1 3. In this problem, the domain of discourse is the set ofall integers. Which statements are true? If an existential statement is true, give an example. If a universal statement is false, give a counterexample. (4 pts) a. ax(xx-1)