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(Q- P) `

Answer

To solve the problem step by step, we will use the information provided about the sets P and Q.

### Step 1: Understand the given information
We have the following information:
- \( n(P \cup Q) = 70 \) (the number of elements in the union of sets P and Q)
- \( n(P) = 45 \) (the number of elements in set P)
- \( n(Q) = 38 \) (the number of elements in set Q)

### Step 2: Draw the Venn Diagram
1. Draw two overlapping circles, one for set P and one for set Q.
2. Label the left circle as P and the right circle as Q.
3. The area where the two circles overlap represents the elements that are in both sets P and Q.

### Step 3: Use the formula for the union of two sets
The formula for the union of two sets is given by:
\[ n(P \cup Q) = n(P) + n(Q) - n(P \cap Q) \]
Where \( n(P \cap Q) \) is the number of elements in both sets.

### Step 4: Substitute the known values into the formula
We can substitute the known values into the formula:
\[ 70 = 45 + 38 - n(P \cap Q) \]

### Step 5: Solve for \( n(P \cap Q) \)
Now, we simplify the equation:
\[ 70 = 83 - n(P \cap Q) \]
Rearranging gives:
\[ n(P \cap Q) = 83 - 70 \]
\[ n(P \cap Q) = 13 \]

### Step 6: Find \( n(Q - P) \)
The number of elements in set Q that are not in set P (denoted as \( n(Q - P) \)) can be calculated using the formula:
\[ n(Q - P) = n(Q) - n(P \cap Q) \]
Substituting the known values:
\[ n(Q - P) = 38 - 13 \]
\[ n(Q - P) = 25 \]

### Conclusion
The number of elements in set Q that are not in set P is \( n(Q - P) = 25 \).