Question

Let \( A = \{1, 2\}, B = \{3, 4\} \), then the number of relations from A to B is:

• A. 2
• B. \( 2^2 \)
• C. \( 2^3 \)
• D. \( 2^4 \)

Hint:

To find the number of relations between two sets, use the formula \( 2^{|A| \times |B|} \), where \( |A| \) and \( |B| \) are the sizes of the sets.

Answer 1

The Correct Option is D

Step 1: Understanding the number of relations.
The number of relations between two sets \( A \) and \( B \) is given by \( 2^{|A| \times |B|} \), where \( |A| \) and \( |B| \) represent the number of elements in sets \( A \) and \( B \), respectively.
Step 2: Applying the formula.
Here, \( |A| = 2 \) and \( |B| = 2 \), so the number of relations from \( A \) to \( B \) is: \[ 2^{|A| \times |B|} = 2^{2 \times 2} = 2^4 \]
Step 3: Conclusion.
Thus, the number of relations from \( A \) to \( B \) is \( 2^4 \). Final Answer:} \( 2^4 \).