# Singletons — What is a Singleton?

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∶7x-3=11}
(iii) F={y∶2y+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∶7x-3=11}

7x-3=11
7x=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∶2y+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.

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