Use the given information to find the number of elements in each of the regions labeled R1 through R5.
n(A) = 29, n(B) = 33, n(C) = 39, n(A ∩ B) = 15, n(U) = 79

We are tasked with finding the number of elements in each of the five regions \( R_1, R_2, R_3, R_4, R_5 \) using the provided set information.

Here are the known values:
- \( n(A) = 29 \) (number of elements in set \( A \)),
- \( n(B) = 33 \) (number of elements in set \( B \)),
- \( n(C) = 39 \) (number of elements in set \( C \)),
- \( n(A \cap B) = 15 \) (number of elements common to both \( A \) and \( B \)),
- \( n(U) = 79 \) (the total number of elements in the universal set \( U \)).

To clarify, we are dealing with three overlapping sets \( A \), \( B \), and \( C \), where:
- \( R_1 \): elements in \( A \) only,
- \( R_2 \): elements in \( A \cap B \) (common to both \( A \) and \( B \) but not in \( C \)),
- \( R_3 \): elements in \( B \) only,
- \( R_4 \): elements in \( C \),
- \( R_5 \): elements outside of \( A \), \( B \), and \( C \).

We will now proceed to find these values step by step.

1. \( n(A \cup B) \): First, we use the formula for the union of two sets:
\[
n(A \cup B) = n(A) + n(B) - n(A \cap B)
\]
Substitute the given values:
\[
n(A \cup B) = 29 + 33 - 15 = 47
\]
So, there are 47 elements in either \( A \), \( B \), or both.

2. \( n(C) \): There are 39 elements in set \( C \), but we are also interested in the overlap with \( A \cup B \). However, no information is provided for the overlap of \( C \) with \( A \) or \( B \) directly. Since the total number of elements in the universal set \( U \) is given as 79, and we know the number of elements in \( A \cup B \), we can find \( R_5 \).

3. \( n(R_5) \): This is the number of elements outside \( A \), \( B \), and \( C \), i.e., elements in the universal set \( U \) but not in any of the sets \( A \), \( B \), or \( C \):
\[
n(R_5) = n(U) - n(A \cup B \cup C)
\]
At this point, we would need the additional information of how \( C \) overlaps with \( A \) and \( B \) to complete the solution fully.

Would you like me to proceed further with assumptions or clarify any points?

Use the given information to find the number of elements in each of the regions labeled R1 through R5. n(A) = 29, n(B) = 33, n(C) = 39, n(A ∩ B) = 15, n(U) = 79

Solve a set theory problem involving three overlapping sets A, B, and C. Learn how to calculate the number of elements in regions R1 to R5 using key concepts like union, intersection, and the universal set. This problem is perfect for high school students studying set theory.

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