Which of the following is an infinite set ?

Options

A. `{x : x" is a prime, "x lt 10}`
B. `{ x : x" is a vowel in the word MATHEMATICS"}`
C. `{x : x" is a natural number, "2015 lt x lt 2016}`
D. `{x : x in Z, x" is a non-negative integer"}`

Answer

D

Explanation

(a) `{x : x in N, x" ia a prime, "x lt 10}`
`={2, 3, 5, 7}`
It is finite set.
(b) {x : x is a vowel in the word}
`={A, E, I}`
(c) `{x : x in N, 2015 lt x lt 2016}`
There is no natural number between 2015 and 2016.
`:.` It is an empty set.
`:.` Hence, it is a finite set.
(d) `{x : x in Z," x is a non-negative integer"}`
`={0, 1, 2, 3,...}`
It is an infinite set.
Hence, the correct option is (d)