Set Theory

A singleton set is a set that contains exactly one element. - Option A:

%5C%7B%20x%20%3A%20x%5E2%20%3D%204%2C%20%5C%2C%20x%20%5Cin%20%5Cmathbb%7BR%7D%20%5C%7D

gives two solutions,

x%20%3D%202

and

x%20%3D%20-2

, so it is not a singleton set. - Option B:

%5C%7B%20x%20%3A%20%7Cx%7C%3C4%2C%20%5C%2C%20x%20%5Cin%20%5Cmathbb%7BN%7D%20%5C%7D

includes all natural numbers less than 4, so it contains more than one element. It is not a singleton set. - Option C:

%5C%7B%20x%20%3A%20%7Cx%7C%3C-4%2C%20%5C%2C%20x%20%5Cin%20%5Cmathbb%7BN%7D%20%5C%7D

has no solution, because no natural number satisfies

%7Cx%7C%3C-4

. - Option D:

%5C%7B%20x%20%3A%20x%5E2%20%3D%204%2C%20%5C%2C%20x%20%5Cin%20%5Cmathbb%7BN%7D%20%5C%7D

gives the solution

x%20%3D%202

, which is a singleton set. Therefore, the correct answer is option (D)

Chapter Questions
1 MCQs