If `n ( C cup T ) = 70, n ( C ) = 37 and n ( T ) = 35`. Then, `n ( C cap T)` is equal to

Options

A. 4
B. 8
C. 2
D. 12

Answer

To find \( n(C \cap T) \), we can use the formula for the union of two sets:

\[ n(C \cup T) = n(C) + n(T) - n(C \cap T) \]

We are given the following values:
- \( n(C \cup T) = 70 \)
- \( n(C) = 37 \)
- \( n(T) = 35 \)

Now, we can substitute these values into the formula:

\[ 70 = 37 + 35 - n(C \cap T) \]

Next, we simplify the right side:

\[ 70 = 72 - n(C \cap T) \]

Now, we can isolate \( n(C \cap T) \):

\[ n(C \cap T) = 72 - 70 \]

Calculating the right side gives us:

\[ n(C \cap T) = 2 \]

Thus, the value of \( n(C \cap T) \) is \( 2 \).