Unit 7 Exercises
1. Let Q(x, y) denote the statement "x is greater than y." What are the truth values of the following?
2. Let P(x) be the statement "x is happy," where the universe of discourse for x is the set of students. Express each of the following quantifications in English.
3. Let P(x) be the statement " x > x^{2}." If the universe of discourse is the set of real numbers, what are the truth values of the following?
4. Suppose that the universe of discourse of the atomic formula P(x,y) is {1, 2, 3}. Write out the following propositions using disjunctions andconjunctions.