Question

If \( A \) is the set of odd numbers less than 6 and \( B \) is the set of prime factors of 30, then:

• A. \( A \cup B = \{ 1, 3, 5, 2, 3, 5 \} \)
• B. \( A \cap B = \{ 3, 5 \} \)
• C. \( A \neq B \)
• D. \( A \cup B = \{ 1, 3, 5, 2, 3 \} \)

Hint:

When comparing sets, check if they contain exactly the same elements. If they do, they are equal; otherwise, they are not.

Answer 1

The Correct Option is C

Step 1: Define the sets.
We are given the following sets:
\( A \) is the set of odd numbers less than 6: \[ A = \{ 1, 3, 5 \} \] \( B \) is the set of prime factors of 30. First, find the prime factors of 30: \[ 30 = 2 \times 3 \times 5 \] Thus, \( B = \{ 2, 3, 5 \} \). Step 2: Compare the sets \( A \) and \( B \).
Set \( A = \{ 1, 3, 5 \} \)
Set \( B = \{ 2, 3, 5 \} \)
Clearly, \( A \neq B \) because the elements \( 1 \) and \( 2 \) are not present in both sets. Step 3: Final answer. The correct answer is \( A \neq B \).