Write down all the subsets of the following sets.

(i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) $ϕ$ .

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Solution

(i) Number of elements in given set = 1

Number of subsets of given set = $2^{1} = 2$

$∴$ Subsets of given set are $ϕ,$ {a}.

(ii) Number of elements in given set = 2

Number of subsets of given set = $2^{2} = 4$

$∴$ Subsets of given set are $ϕ,$ {a}, {b}, {a, b}.

(iii) Number of elements in given set = 3

Number of subsets of given set = $2^{3} = 8$

$∴$ Subsets of given set are $ϕ,$ {1}, {2}, {3}, {1, 2}, {2, 3} {1, 3}, {1, 2, 3}.

(iv) Number of elements in given set = 0

Number of subsets of given set = $2^{0} = 1$

$∴$ Subset of given set is $ϕ .$

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