Which of the following is an empty set ?

Options

A. `{x : x in N, x" is divisible by 2"}`
B. `{x : x in N, x" is the additive inverse of "2016}`
C. `{x : x" is a binary digit"}`
D. { x : x is either prime or composite}

Answer

B

Explanation

(a) `{x : x in N, x" is divisible by 2"}`
`={2, 4, 6, ...}`
`:.` It is not an empty set.
(b) `{x : x in N, x" is an additive inverse of "2016}`
Additive inverse of 2016 is but `-2016 notin N`
`:.` It is an empty set.
(c) Binary digits are 0 and 1.
`:.` Given set is not an empty set.
(d) Except 1, every natural number is either prime ot composite.
`:.` Given set is not an empty set.
Hence, the correct option is (b)