**SINGLETON**(noun)

Definition: A set having only one element is called a singleton.

These sets are singletons: (i) *A*={8}, (ii) *B*={*x|x* is an even prime number}→*B*={2}

**Singleton** (noun)

A set, consisting of a single element, is called a singleton.

Example 1. If a set *C* has only one element, we call it a __singleton__. *C*={a}. Thus, {a} is a singleton.

Ex2. The sets {0}, {5}, {-7} are singletons.

Ex3. *D*={*x∶x*+8=0,*x*∈ℤ} is a singleton, because this set contains only one integer, namely -8.

Ex4. Find, which of the following sets are singletons:

(i) The set of points of intersection of two non-parallel straight lines on the same plane.

(ii) *E*={*x*∶7*x*-3=11}

(iii) *F*={*y*∶2*y*+1<3 and *y*∈𝕎}

Solution:

(i) The set of points of intersection of two non-parallel straight lines on the same plane is a singleton.

(ii) *E*={*x*∶7*x*-3=11}

*x*-3=11

7

*x*=11+3

*x*=14÷7=2

*E*={2}

Hence, the given set *E* has only one element, so it is a singleton.

(iii) *F*={*y*∶2*y*+1<3 and *y*∈𝕎}

2y+1<3
2y+1-1<3-1 (Subtracting 1 from both sides)
2y<2 (Dividing both sides by 2)
y<1
F={0} |

Hence, it is a singleton.