Question 6: What is the number of elements of the power set of each of the following sets?
\((iv)\) \(\;\) \(\{a,\{b,c\}\}\)
Solution:
\(n=2\)
\(2^2=4\)
There are \(4\) 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: \(a\) \(\quad\) second element: \(\{b,c\}\)
In this case there are 2 element. So, \(n=2\) and we have \(2^2=4\) number of elements in the power set.