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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.
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B
A={x:7x3=11}
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C
B={y:2y+1<3 and yW}
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D
C={Set of even prime numbers greater than 2}
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Solution

The correct options are
B A={x:7x3=11}
C B={y:2y+1<3 and yW}

(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:7x3=11} 7x3=11 7x=11+3 7x=14 x=147=2 A={2}Hence, the given set is a singleton set. (iii)B={y:2y+1<3 and y W}2y+1<3 2y+11<31 (Subtracting 1 from both sides) 2y<2 y<22 (Dividing both sides by 2) y<1 B={0}Hence, it is a singleton set.

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


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