Question 23 of 47beginner🔧 ApplyShort Answer2 marks

Write down all the subsets of the following sets:

(i)

{a}

Answer

The subsets of {a} are φ and {a}.

(ii)

{a, b}

Answer

The subsets of {a, b} are φ, {a}, {b}, and {a, b}.

(iii)

{1, 2, 3}

Answer

The subsets of {1, 2, 3} are φ, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}.

(iv)

φ

Answer

The subset of φ is φ.

Explanation

The question asks for the list of all subsets for given sets. Based on the concept of subsets introduced in the context (Section 1.6), a set is a subset of itself, and the empty set φ is a subset of every set. For a set with n elements, the number of subsets is 2n2^{n}. Part (i) has 1 element (2 subsets), part (ii) has 2 elements (4 subsets), part (iii) has 3 elements (8 subsets), and part (iv) is the empty set (1 subset).