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

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Solution

If set $A$ is sub set of set $B$ then all the elements of set $A$ must be present in set $B$ .
Null set $(ϕ$ ) be always subset of any set.
(i) Given set ${a}$
The possible subsets of given sets are $ϕ, {a}$ .
(ii) Given set ${0, 1}$
The possible subsets of given sets are $ϕ, {0}, {1}, {0, 1}$
(iii) Given set ${a, b, c}$
The possible subsets are $ϕ, {a}, {b}, {c}, {a, b}, {b, c}, {c, a}, {a, b, c}$
(iv) Given set ${1, {1}}$
The possible subsets are $ϕ, {1}, {{1}}, {1, {1}}$
(v) Given set ${ϕ}$
The possible subsets are $ϕ, {ϕ}$

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