2. If set A has 4 elements and B has 3 elements then set n(A X B) is?a) 12b) 14c) 24d) 7

1. Break Down the Problem

We need to determine the number of elements in the Cartesian product of sets A and B, denoted as $n(A \times B)$. The Cartesian product of two sets $A$ and $B$ contains all ordered pairs where the first element is from set $A$ and the second element is from set $B$.

2. Relevant Concepts

The formula to find the number of elements in the Cartesian product of two sets is: $n(A \times B) = n(A) \times n(B)$ where $n(A)$ is the number of elements in set $A$ and $n(B)$ is the number of elements in set $B$.

3. Analysis and Detail

Given:

• $n(A) = 4$ (since set A has 4 elements)
• $n(B) = 3$ (since set B has 3 elements)

Now, applying the formula: $n(A \times B) = n(A) \times n(B) = 4 \times 3$ Calculating this gives: $n(A \times B) = 12$

4. Verify and Summarize

We calculated the number of elements in the Cartesian product to be 12. To summarize, the operation is straightforward: multiply the number of elements in each set to get the result.

Final Answer

The number of elements in $n(A \times B)$ is 12. Thus, the correct option is a) 12.