JAMIA 2025 — Mathematics PYQ

The Power Set $P(A)$ of a set $A$ is the set of all possible subsets of $A$, including the empty set $\varnothing$ and the set $A$ itself.

If the order (cardinality) of set $A$ is $n$:

Then the order of the power set $P(A)$ is given by the formula:

Proof / Logic

To understand why the order is $2^n$, consider that for every element in set $A$, there are exactly 2 choices when forming a subset:

1. The element is included in the subset.

2. The element is excluded from the subset.

Since there are $n$ independent elements, each with 2 choices, the total number of ways to form a subset is:

Example

If $A=\{1,2\}$, then $n=2$.

The subsets are $\varnothing ,\{1\},\{2\},\{1,2\}$.

The number of subsets is:

Final Answer:

The order of the power set $P(A)$ is $2^n$.