Question

Which of the following sets is a finite set?

• A. A = \\{x : x \in Z and x^2 - 5x + 6 = 0\\}
• B. B = \\{x : x \in Z and $x^2$ is even\\}
• C. D = \\{x : x \in Z and x > \- 10\\}
• D. All of these

Answer 1

Answer: (A)

A = \\{x : x \in Z and x^2 - 5x + 6 = 0\\}

Answer 2

(a) $A = |x : x \in Z$ and x^2 - 5x + 6 = 0\\} = \\{2, 3\\} So, $A$ is a finite set. (b) 8 = \\{ x : x \in Z and $x^2$ is even\\} = \\{...,-4, -2,0,2,4, ...\\} Clearly, $B$ is an infinite set. (c) D = \\{x : x \in Z and x > -10\\} = \\{-9, -8, -7,...\\} Clearly, $D$ is an inlinite set.