Let P and Q be two sets such that `n(P uu Q) = 70 ,n (P )= 45 and n(Q) = 38, ` Draw a Venn diagram and find :
` n(P-Q) `

Answer

To solve the problem, we need to find \( n(P - Q) \) given the values of \( n(P \cup Q) \), \( n(P) \), and \( n(Q) \). Here’s a step-by-step solution:

### Step 1: Understand the given information
We have the following:
- \( n(P \cup Q) = 70 \)
- \( n(P) = 45 \)
- \( n(Q) = 38 \)

### Step 2: Use the formula for the union of two sets
We know the formula for the union of two sets:
\[ n(P \cup Q) = n(P) + n(Q) - n(P \cap Q) \]
Substituting the known values into the formula:
\[ 70 = 45 + 38 - n(P \cap Q) \]

### Step 3: Simplify the equation
Combine the values on the right side:
\[ 70 = 83 - n(P \cap Q) \]

### Step 4: Solve for \( n(P \cap Q) \)
Rearranging the equation gives:
\[ n(P \cap Q) = 83 - 70 \]
\[ n(P \cap Q) = 13 \]

### Step 5: Find \( n(P - Q) \)
We know that:
\[ n(P - Q) = n(P) - n(P \cap Q) \]
Substituting the values we have:
\[ n(P - Q) = 45 - 13 \]
\[ n(P - Q) = 32 \]

### Step 6: Conclusion
Thus, the value of \( n(P - Q) \) is \( 32 \).

### Venn Diagram
To visualize this, draw two overlapping circles labeled P and Q. The area of intersection (where both circles overlap) represents \( n(P \cap Q) = 13 \). The area of circle P that does not overlap with Q represents \( n(P - Q) = 32 \), and the area of circle Q that does not overlap with P represents \( n(Q - P) = 25 \) (which can be calculated as \( n(Q) - n(P \cap Q) = 38 - 13 \)).