9. Prove that the following kogical expressions aro logically equivalent by applying the law of logic 10. Give a logical expression with variables p, q, and r that's true only if p and q are false and r is true. 11. Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Qlx): x is a perfect square Are the following logical expressions propositions? If the answer is yes, indicate whether the statement is true or false. a PR) b. P(2) 12. Consider the following statements in English. Write a logical expression with the same meaning. The domain of discourse must be the set of all real numbers. a. There is a number whose cube is equal to -2 b. The reciprocal of every number between O and 1 is greater than 1. 5