Find the value of​ n(A) if

​n(B)equals=3737​,

​n(A

intersect∩

​B)equals=1414​,

and​ n(A

union∪

​B)equals=6060.

To find the value of \( n(A) \), we can use the formula for the union of two sets:

\[
n(A \cup B) = n(A) + n(B) - n(A \cap B)
\]

We are given:
- \( n(B) = 37 \)
- \( n(A \cap B) = 14 \)
- \( n(A \cup B) = 60 \)

Substituting the known values into the formula, we have:

\[
60 = n(A) + 37 - 14
\]

Simplify:

\[
60 = n(A) + 23
\]

Subtract 23 from both sides:

\[
n(A) = 60 - 23
\]

\[
n(A) = 37
\]

Therefore, the value of \( n(A) \) is:

\[
\boxed{37}
\]

Would you like further details or have any questions about this solution?

Here are 5 related questions:
1. What is the formula for the intersection of two sets if all other values are known?
2. How do you find the number of elements in the complement of a set?
3. Can this method be used for more than two sets? If so, how does it change?
4. What does \( n(A \cup B) \) represent in set theory?
5. How would you find \( n(A \setminus B) \) using the given information?

**Tip:** When solving problems involving sets, drawing a Venn diagram can be very helpful to visualize the relationships and intersections between sets.

Find the value of n(A) if n(B) = 37, n(A ∩ B) = 14, and n(A ∪ B) = 60.

Discover how to calculate n(A) using set theory concepts, given n(B) = 37, n(A ∩ B) = 14, and n(A ∪ B) = 60. This problem involves the principle of inclusion-exclusion and set union and intersection formulas, suitable for students in Grades 7-9.

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