If A={1, 3, 5, 7}, then what is the cardinality of the power set P(A)?

Options

A. 8
B. 15
C. 16
D. 17

Explanation

To find the cardinality of the power set \( P(A) \) of the set \( A = \{1, 3, 5, 7\} \), we can follow these steps:

### Step 1: Identify the elements in set A
The set \( A \) contains the elements:
\[ A = \{1, 3, 5, 7\} \]

### Step 2: Determine the number of elements in set A
Count the number of elements in set \( A \):
- The elements are 1, 3, 5, and 7.
- Therefore, the number of elements in \( A \) is \( n(A) = 4 \).

### Step 3: Use the formula for the cardinality of the power set
The cardinality of the power set \( P(A) \) is given by the formula:
\[ |P(A)| = 2^{n(A)} \]
where \( n(A) \) is the number of elements in set \( A \).

### Step 4: Calculate the cardinality of the power set
Substituting the value of \( n(A) \):
\[ |P(A)| = 2^{4} \]
\[ |P(A)| = 16 \]

### Conclusion
The cardinality of the power set \( P(A) \) is \( 16 \).

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