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The image shows a mathematical problem which asks the user to "Let A be a set. Suppose the cardinality of set A is 6. Enumerate the number of subsets of the set A that contain two elements."

To solve this problem, let's break it down:

1. **Cardinality of Set A**: The set A has 6 elements, which means \( |A| = 6 \).

2. **Subsets of A with Two Elements**: We are asked to find the number of subsets of A that contain exactly two elements.

The number of subsets with exactly two elements is given by the combination formula:

\[
\text{Number of subsets} = \binom{n}{k} = \frac{n!}{k!(n-k)!}
\]

where:
- \( n \) is the total number of elements in the set \( A \) (which is 6),
- \( k \) is the number of elements in each subset (which is 2 in this case).

So, we calculate:

\[
\binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15
\]

Therefore, there are 15 subsets of set A that contain exactly two elements.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What is the total number of subsets of a set with 6 elements?
2. How many subsets of set A have at least two elements?
3. If a set has 10 elements, how many subsets of exactly 3 elements can be formed?
4. Can you determine the number of subsets of a set that have exactly one element?
5. What is the relationship between the cardinality of a set and the number of subsets?

**Tip:** Understanding the combination formula is key to solving problems involving subsets of a set with a specific number of elements.

Let A be a set. Suppose the cardinality of set A is 6. Enumerate the number of subsets of the set A that contain two elements.

Learn how to calculate the number of subsets of a set with 6 elements, focusing on subsets containing exactly two elements. This problem covers key concepts in set theory and combinatorics, using the combination formula. Suitable for students in Grades 9-10.

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