Question 6: What is the number of elements of the power set of each of the following sets?
\((iv)\) \(\;\) \(\{\{a,b\},\{b,c\},\{d,e\}\}\)
Solution:
\(n=3\)
\(2^3=8\)
There are \(8\) element in the power set.
Explanation:
If a set has \(n\) elements, then the number of elements in its power set is \(2^n\).
First element: \(\{a,b\}\) \(\quad\) Second element: \(\{b,c\}\) \(\quad\) Third element: \(\{d,e\}\)
In this case there are 3 element. So, \(n=3\) and we have \(2^3=8\) number of elements in the power set.