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 are tasked with identifying the incorrect statement from a set of options regarding these sets.

### Step 1: Calculate \( n(A \cup B) \)

Using the formula for the union of two sets:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]

Substituting the known values:
\[ n(A \cup B) = 7 + 13 - 5 = 15 \]

### Step 2: Calculate \( n(A - B) \)

The number of elements in set A that are not in set B can be calculated as:
\[ n(A - B) = n(A) - n(A \cap B) \]

Substituting the known values:
\[ n(A - B) = 7 - 5 = 2 \]

### Step 3: Calculate \( n(B - A) \)

The number of elements in set B that are not in set A can be calculated as:
\[ n(B - A) = n(B) - n(A \cap B) \]

Substituting the known values:
\[ n(B - A) = 13 - 5 = 8 \]

### Step 4: Check the options

1. **Option 1**: \( n(A \cup B) = 15 \) (This is correct)
2. **Option 2**: \( n(A - B) = 7 - 13 = -6 \) (This is incorrect since the number of elements cannot be negative)
3. **Option 3**: \( n(A) \times n(B) = 7 \times 13 = 91 \) (This is correct)
4. **Option 4**: \( n(A \cup B) \times n(A \cap B) = 15 \times 5 = 75 \) (This is correct)

The incorrect statement is from **Option 2**, where \( n(A - B) \) is calculated incorrectly as -6.

### Summary of the Solution
The incorrect statement is that \( n(A - B) = -6 \).