Let P(x) be given by "x is a prime number," where the domain of x is the set of all positive integers less than 30. Recall that a prime number is an integer that is only divisible by 1 and itself. The integer 1 is not defined to be prime. (a) Is P(x) a propositional function? Explain. (b) Find all x such that P(x) is false. Let Q(x,y) be given by "x² + y² ≤ 4" where x, y € Z. Find all ordered pairs (x, y) for which Q(x, y) is true.
Let P(x) be given by "x is a prime number," where the domain of x is the set of all positive integers less than 30. Recall that a prime number is an integer that is only divisible by 1 and itself. The integer 1 is not defined to be prime. (a) Is P(x) a propositional function? Explain. (b) Find all x such that P(x) is false. Let Q(x,y) be given by "x² + y² ≤ 4" where x, y € Z. Find all ordered pairs (x, y) for which Q(x, y) is true.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 39E
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![1. Let P(x) be given by "x is a prime number," where the domain of x is the set of all positive
integers less than 30. Recall that a prime number is an integer that is only divisible by 1 and
itself. The integer 1 is not defined to be prime.
(a) Is P(x) a propositional function? Explain.
(b) Find all x such that P(x) is false.
2. Let Q(x,y) be given by “x² + y² ≤ 4" where x, y € Z. Find all ordered pairs (x, y) for
which Q(x, y) is true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d696bc1-45d5-4770-8c5d-7ee4498a818a%2Fb1de3f2f-c0e2-4cbd-b02b-0eeffa304b93%2F9drab6v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let P(x) be given by "x is a prime number," where the domain of x is the set of all positive
integers less than 30. Recall that a prime number is an integer that is only divisible by 1 and
itself. The integer 1 is not defined to be prime.
(a) Is P(x) a propositional function? Explain.
(b) Find all x such that P(x) is false.
2. Let Q(x,y) be given by “x² + y² ≤ 4" where x, y € Z. Find all ordered pairs (x, y) for
which Q(x, y) is true.
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