If A, B and C are three sets and U is the universal set such that n(U)=700, n(A)=200, n(B)=300 and `n(AnnB)=100`, then what is the value of `(A'nnB')`?

Options

A. 100
B. 200
C. 300
D. 400

Explanation

To find the value of \( n(A' \cap B') \), we can follow these steps:

### Step 1: Understand the given information
We have the following values:
- \( n(U) = 700 \) (the number of elements in the universal set)
- \( n(A) = 200 \) (the number of elements in set A)
- \( n(B) = 300 \) (the number of elements in set B)
- \( n(A \cap B) = 100 \) (the number of elements in the intersection of sets A and B)

### Step 2: 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 values:
\[ n(A \cup B) = 200 + 300 - 100 = 400 \]

### Step 3: Calculate \( n(A' \cap B') \)
The complement of the union of sets A and B gives us the intersection of their complements:
\[ n(A' \cap B') = n(U) - n(A \cup B) \]
Substituting the values we found:
\[ n(A' \cap B') = 700 - 400 = 300 \]

### Final Answer
Thus, the value of \( n(A' \cap B') \) is \( 300 \).

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