Sets-Relations-And-Functions Question 134
Question: Which of the following is a singleton set?
Options:
A) $ \{x:| x |=5,x\in N\} $
B) $ \{x:| x |=6,x\in Z\} $
C) $ \{x:x^{2}+2x+1=0,x\in N\} $
D) $ \{x:x^{2}=7,x\in N\} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a]a. $ | x |=5\Rightarrow x=5[\because x\in N] $
$ \therefore $
Given set is singleton.
b. $ | x |=6\Rightarrow x=-6,,6[\because x\in Z] $
$ \therefore $
Given set is not singleton.
c. $ x^{2}+2x+1=0\Rightarrow {{(x+1)}^{2}}=0 $
$ \Rightarrow x=-1,-1 $
Since, $ -1\notin N, $
$ \therefore $
given set $ =\phi $ d. $ x^{2}=7\Rightarrow x=\pm \sqrt{7}. $
BETA
