If `n(AnnB)=20`, `n(AnnBnnC)=5`, then `n(Ann(B-C))` is

Options

A. `15`
B. `10`
C. `5`
D. `20`

Answer

To solve the problem step by step, we will use the information provided and the formula for set operations.

### Step 1: Understand the given information
We are given:
- \( n(A \cap B) = 20 \) (the number of elements in the intersection of sets A and B)
- \( n(A \cap B \cap C) = 5 \) (the number of elements in the intersection of sets A, B, and C)

### Step 2: Recall the formula for \( n(A \cap (B - C)) \)
We need to find \( n(A \cap (B - C)) \). The formula for this is:
\[ n(A \cap (B - C)) = n(A \cap B) - n(A \cap B \cap C) \]
This formula tells us that to find the number of elements in the intersection of A and B excluding those that are also in C, we subtract the number of elements that are in all three sets (A, B, and C) from the number of elements in A and B.

### Step 3: Substitute the values into the formula
Now we can substitute the values we have into the formula:
\[ n(A \cap (B - C)) = n(A \cap B) - n(A \cap B \cap C) = 20 - 5 \]

### Step 4: Perform the calculation
Now, we perform the subtraction:
\[ n(A \cap (B - C)) = 20 - 5 = 15 \]

### Step 5: Conclusion
Thus, the number of elements in \( n(A \cap (B - C)) \) is 15.

### Final Answer
The answer is \( 15 \).

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