Question

The number of elements in the power set P(s) of the get $S = \\{ (\phi ),1(2,3)\\}$is:
A). 2
B). 4
C). 8
D). None of these

Answer 1

Here the given question need to write the number of elements in the given set, and here we can see that in the given set we have four elements, but one element which is represented as phy, is known as null or empty element hence not count for in the number of elements. And for the elements in the power set we need to use the formula for that.
Formulae Used: Element in the power set, for the given set with “n” elements would be given by:
$\Rightarrow {2^n}$

Complete step-by-step solution:
Here to solve the given question we need to understand that the element of set is counted, by the number of element present in the set and here we can see that three elements are present that is:
$\Rightarrow (\phi ),1(2,3)$
But here the element “$\phi$” is known as a null or empty set, hence not counted as an element for the given set, so the number of elements in this set are three.
Hence the elements in the power set is given by:
$\Rightarrow {2^3} = 8$
Hence eight elements would be there in the power set for the given set.

Note: In the set theory, we need to decide the set element on the basis of the elements present in the set, we can see that, three element are present, and other one is the empty or null element which give the answer that there are three element in the set.