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Question

State which of the following sets are singleton sets.
(i) A={x|x=16}
(ii) B={y|y2=36}
(iii) C={p|pI,p3=8}
(iv) D={q|(q4)2=0}
(v) E={x|1+2x=3x,xW}

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Solution

Singleton set: A set that contains a single element is called a singleton set.
(i) A={x|x=16}

Roster form of set A={16}
This set consists of only one element. Therefore, it is a singleton set.
(ii) B={y|y2=36}

Since, y2=36

y=±6

Roster form of set B={+6, 6}
This set consists of two elements. Therefore, it is not a singleton set.
(iii) C={p|pI,p3=8}

Since, p3=8

p3=(2)3

p=2

Roster form of set C={2}
This set consists of only one element. Therefore, it is a singleton set.

(iv) D={q|(q4)2=0}

Since, (q4)2=0

q4=0

q=4

Roster form of set D={4}
This set consists of only one element. Therefore, it is a singleton set.
(v) E={x|1+2x=3x,xW}
Since, 1+2x=3x,xW

2x3x=1

x=1

x=1

Roster form of set E={1}
This set consists of only one element. Therefore, it is a singleton set.


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