Question

Which of the following sets are singleton sets?

• A. The set of points of intersection of two parallel straight lines in the same plane.
• B. $A=\{x:7x-3=11\}$
• C. $B=\{y:2y+1<3andy\in W\}$
• D. $C=\left\{\text{Set of even prime numbers greater than 2}\right\}$

Answer 1

Answer: (B), (C)

The correct options are
B $A=\{x:7x-3=11\}$
C $B=\{y:2y+1<3andy\in W\}$

(i) Two parallel straight lines in the same plane never intesect. So, the set of points of intersection of two parallel straight lines in the same plane is a null set.

(ii)$A=\{x:7x-3=11\}7x-3=11\Rightarrow 7x=11+3\Rightarrow 7x=14\Rightarrow x=\frac{14}{7}=2\therefore A=\left\{2\right\}\text{Hence, the given set is a singleton set.}\left(iii\right)B=\{y:2y+1<3andy\in W\}2y+1<3\Rightarrow 2y+1-1<3-1\text{(Subtracting 1 from both sides)}\Rightarrow 2y<2\Rightarrow y<\frac{2}{2}\text{(Dividing both sides by 2)}\Rightarrow y<1\therefore B=\left\{0\right\}\text{Hence, it is a singleton set.}$

(iv) There are no even prime numbers which are greater than 2. So, it is a null set.