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The question you're asking is about how many relations are possible between two sets.

Let:
- Set \( A \) have 3 elements.
- Set \( B \) have 2 elements.

### Concept:

A **relation** from set \( A \) to set \( B \) is any subset of the Cartesian product \( A \times B \). The number of elements in \( A \times B \) is given by the product of the number of elements in \( A \) and \( B \).

\[
\text{Number of elements in } A \times B = |A| \times |B| = 3 \times 2 = 6
\]

For each pair in \( A \times B \), there are 2 possibilities: either the pair is included in the relation, or it is not included.

Therefore, the total number of possible relations is:
\[
2^{|A \times B|} = 2^6 = 64
\]

### Answer:
The correct option is **d) 64**.

Would you like further details, or have any questions?

Here are five related questions to expand on this topic:
1. What is the definition of a Cartesian product of two sets?
2. How can we represent a relation from set \( A \) to set \( B \) graphically?
3. What is the difference between a relation and a function?
4. How would the number of possible relations change if both sets \( A \) and \( B \) had the same number of elements?
5. Can a relation from set \( A \) to set \( B \) be a one-to-one relation?

**Tip:** The number of relations depends on the number of pairs in the Cartesian product of the two sets. Always remember this when calculating possible relations.

If set A has 3 elements and set B has 2 elements, then how many relations are possible?

Learn how to calculate the number of possible relations between two sets. In this problem, Set A has 3 elements, and Set B has 2 elements. Understand the concept of relations and Cartesian products in set theory. Suitable for students in Grades 9-12.

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