Let A be the set of all positive prime intergers less than 30. The number of different rational numbers whose numerator and denominator belong to A is

Options

A. 90
B. 180
C. 91
D. none of these

Explanation

To solve the problem, we need to determine the number of different rational numbers that can be formed using the positive prime integers less than 30 as both the numerator and the denominator. Here’s a step-by-step solution:

### Step 1: Identify the set of prime numbers less than 30
The prime numbers less than 30 are:
\[ A = \{2, 3, 5, 7, 11, 13, 17, 19, 23, 29\} \]

### Step 2: Count the number of elements in set A
The number of elements (cardinality) in set A is:
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