r : If a finite set has n elements then its total number of substets is `2^n`
Converse of statement r is

Options

A. If a finite set has n elements then its number of subset is not equal to `2^n`
B. If a finite set has not n elements then its number of subset is equal to `2^n`
C. If number of subset of a finite set in not `2^n` than it is not finite
D. If number of substets of a finite set is `2^n` then it has n elements

Answer

To find the converse of the statement "If a finite set has n elements, then its total number of subsets is \(2^n\)", we need to follow these steps:

### Step-by-Step Solution:

1. **Identify the Original Statement**:
The original statement can be expressed in the form "If P, then Q", where:
- P: A finite set has n elements.
- Q: The total number of subsets is \(2^n\).

2. **Formulate the Converse**:
The converse of a statement "If P, then Q" is "If Q, then P". Thus, the converse of our statement will be:
- If the total number of subsets is \(2^n\), then a finite set has n elements.

3. **Write the Converse Statement**:
Therefore, the converse statement is:
"If the total number of subsets is \(2^n\), then a finite set has n elements."

4. **Analyze the Converse**:
We need to check if this converse statement is true. If a set has \(2^n\) subsets, it implies that the set must have n elements, as the number of subsets of a set is determined by the formula \(2^n\).

5. **Conclusion**:
The converse statement is valid, as it correctly reflects the relationship between the number of subsets and the number of elements in a finite set.

### Final Answer:
The converse of the statement "If a finite set has n elements, then its total number of subsets is \(2^n\)" is:
"If the total number of subsets is \(2^n\), then a finite set has n elements."

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