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

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

(iii) {a, b, c} (iv) {1, {1}}

(v) { $ϕ$ }

Open in App

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}.

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

(v) The set has element, so power set has $2^{1} = 2$ elements, namely $ϕ$ , { $ϕ$ }.

Suggest Corrections

Similar questions

Write down all possible subsets of each of the following sets:
(i) ${a}$ ,
(ii) ${0, 1}$
(iii) ${a, b, c}$
(iv) ${1, {1}}$
(v) ${ϕ}$

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

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

(iii) {a, b, c}

Write down all the subsets of the following sets.

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

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

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

(iii) {1}

0

Join BYJU'S Learning Program