Please I need answers to these questions (1,3,3,4,5 and 6) thank you

8:40 1, Predicates P and Q are defined below, The domain of discourse is the set of all positive integers. P(x): x is prime Q(x): x is a perfect square Are the following logical expressions propositions? If the answer is yes, indicate whether the statement is true or false. (3 pts) a. P(x) b. P(2) 2. 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. (4 pts) a. There is a number whose cube is equal to -2 b. The reciprocal of every number between 0 and l is greater than I 3. In this problem, the domain of discourse is the set of all integers. Which statements are true? If an existential statement is true, give an example. Ifa universal statement is false, give a counterexample. (4 pts) 4. In the following question, the domain of discourse is a set of students who attend a school. Define the following predicates: E(x): x is enrolled in the class. T(x): x took the test Translate the following English statements into a logical expression with the same meaning: (5 pts) a. Someone took the test who is not enrolled in the class. 8:41 1 b. All enrolled students took the test. c.Everyone who took the test is enrolled d. No one took the test. e. At least one enrolled student did not take the test. 5. Determine the truth value of each expression below if the domain is the set of all real numbers. (4 pts) a. axvy (xy-0) example.) (If true, give an (If false, give a counterexample.) (If false, give a counterexample.) d 3yazy-If true, give an example.) 6. Redo the above (problem I), with the domain of positive integers. (4 pts) b. C. d