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

(i) {1, 2} (ii) {1, 2, 3}

(iii) {1}

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Solution

(i) We know that if A is a set and B a subset of A, then B is called a proper subset of A is $B ⊈ A$ and $B \neq A$ , $ϕ$ and is written as $B \subset A$ or $B ⊈ A$ .

Hence, the proper subsets are given by {1}, {2}.

(ii) The proper subsets are given by {1}, {2}, {3}, {1,2}, {2, 3}, {1, 3}.

(iii) The only subsets of the given set are $ϕ$ and {1}.

Hence, there are no proper subsets.

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