For two sets A and B, if `n(A)=7, n(B)=13 and n (AnnB)=5`, then the incorrect statement is

Options

A. `n (A uu B)=15`
B. `n(A-B)=6`
C. `n (AxxB)=91`
D. `n{(AuuB)xx(AnnB)}=75`

Answer

To solve the problem, we need to analyze the information given about the two sets A and B. We know the following:

- \( n(A) = 7 \) (the number of elements in set A)
- \( n(B) = 13 \) (the number of elements in set B)
- \( n(A \cap B) = 5 \) (the number of elements in the intersection of sets A and B)

We need to determine which of the given statements about these sets is incorrect.

### Step-by-Step Solution:

1. **Calculate \( n(A \cup B) \)**:
The formula for the union of two sets is given by:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
Substituting the values we have:
\[ n(A \cup B) = 7 + 13 - 5 = 15 \]

2. **Check Statement A**:
Statement A claims \( n(A \cup B) = 15 \). From our calculation, this is correct.

3. **Calculate \( n(A - B) \)**:
The number of elements in set A that are not in set B is given by:
\[ n(A - B) = n(A) - n(A \cap B) \]
Substituting the values we have:
\[ n(A - B) = 7 - 5 = 2 \]

4. **Check Statement B**:
Statement B claims \( n(A - B) = 6 \). From our calculation, this is incorrect since \( n(A - B) = 2 \).

5. **Calculate \( n(A \times B) \)**:
The number of elements in the Cartesian product of sets A and B is given by:
\[ n(A \times B) = n(A) \times n(B) \]
Substituting the values we have:
\[ n(A \times B) = 7 \times 13 = 91 \]

6. **Check Statement C**:
Statement C claims \( n(A \times B) = 91 \). From our calculation, this is correct.

7. **Check Statement D**:
Statement D claims \( n(A \cup B) - n(A \cap B) = 75 \). We already calculated \( n(A \cup B) = 15 \) and \( n(A \cap B) = 5 \):
\[ n(A \cup B) - n(A \cap B) = 15 - 5 = 10 \]
Hence, Statement D is also incorrect.

### Conclusion:
The incorrect statements are B and D. However, since the question asks for one incorrect statement, we can conclude that Statement B is incorrect.