Question

Classify the following sets as 'singleton' or 'empty'.
(i) A = {x|x is a negative natural number}
(ii) B = {y|y is an odd prime number < 4}
(iii) C = {z|z is a natural number, 5 < x < 7}.
(iv) D = {d|d $\in$ N, d² $\le$ 0}

Answer 1

We have to classify whether the following sets are singleton or empty:

(i) A = $\mathrm{\varphi }$
There isn't any number which is a natural number and negative.
∴ This is an empty set.

(ii) B = {3}
This set consists of only one element .
∴ It is a singleton set.

(iii) C = { 6}
This set consists of only one element.
∴ It is a singleton set.

(iv) D = $\mathrm{\varphi }$
This set does not contain any element.
∴ It is an empty set.