Write down all possible subsets of each of the following sets :

(i) {a} (ii) {0, 1}

(iii) {a, b, c}

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Solution

(i) We know that , if a set has n eleents, then its power set has $2^{n}$ elements. Hence, n= 1, so there $2^{1} = 2$ subsets of the given set. The possible subsets are $ϕ$ , {a}.

(ii) The set has two elements, so power set has $2^{2} = 4$ elements, namely $ϕ$ , {0}, {1}, {0, 1}.

(iii) The set has 3 elements, so power set has $2^{3} = 8$ elements, namely $ϕ$ , {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}.

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