HOMEWORK 4
Question 1. Determine the truth values of the following expressions.
(1) Let P(x) be "x is a prime number". Then the truth value of P(233) is ___.
(2) Let P(x) be "x is a complete square". Then the truth value of P(225) is ___.
(3) Let P(x, y, z) be "x, y, and z are the three sides of a right triangle". Then the truth value of P(5, 12, 13) is ___.
Question 2. Determine the truth values of the following quantified predicates.
(1) Let P(x) be "x is a solution to the equation x^2 - 7x + 10 = 0" with a domain as {1, 3, 5, -2}. Then the truth value of ∃xP(x) is ___.
(2) Let P(x) be "x(x + 1) is an even number" with a domain as {17, 23, 51, 72, 81}. Then the truth value of ∀xP(x) is ___.
(3) Let P(x) be "x > 1/x" with a domain as all the positive real numbers. Then the truth value of ∀xP(x) is ___.
In the following two questions, write A for ∀, and E for ∃
Question 3. Given a statement "Every student in this class has studied calculus". Let C(x) be "x has studied calculus", then the sentence can be translated into ___xC(x). The negation of it can be written as ___x