Question

Write down the power set of the following sets:
(i) A = {a,b} (ii) B = {1,2,3} (iii) D = {p,q, 1,5}
(iv) E=0​

Answer 1

The power set of a given set is the set of all subsets of the given set.

If the given set contains $n$ elements, its power set contains $2^n$ elements.

(i) Given set is,

$\longrightarrow A=\{a,\ b\}$

No. of elements = 2.

Then its power set is,

$\longrightarrow P(A)=\{\phi,\ \{a\},\ \{b\},\ \{a,\ b\}\}$

No. of elements $=2^2=4.$

(ii) Given set is,

$\longrightarrow B=\{1,\ 2,\ 3\}$

No. of elements = 3.

Then its power set is,

$\longrightarrow P(B)=\{\phi,\ \{1\},\ \{2\},\ \{3\},\ \{1,\ 2\},\ \{2,\ 3\},\ \{1,\ 3\},\ \{1,\ 2,\ 3\}\}$

No. of elements $=2^3=8.$

(iii) Given set is,

$\longrightarrow D=\{p,\ q,\ 1,\ 5\}$

No. of elements = 4.

Then its power set is,

$\begin{aligned}\longrightarrow P(D)=\ \ &\{\phi,\ \{p\},\ \{q\},\ \{1\},\ \{5\},\ \{p,\ q\},\ \{p,\ 1\},\ \{p,\ 5\},\ \{q,\ 1\},\\&\{q,\ 5\},\ \{1,\ 5\},\ \{p,\ q,\ 1\},\ \{p,\ q,\ 5\},\ \{p,\ 1,\ 5\},\\&\{q,\ 1,\ 5\},\ \{p,\ q,\ 1,\ 5\}\}\end{aligned}$

No. of elements $=2^4=16.$

(iv) Given set is,

$\longrightarrow E=\phi$

No. of elements = 0.

Then its power set is,

$\longrightarrow P(E)=\{\phi\}$

No. of elements $=2^0=1.$