If `n ( A cup B ) = 727 , n ( A ) = 600 and n ( A cap B) = 127`. Then, `n ( B )` is equal to

Options

A. 324
B. 292
C. 254
D. 236

Answer

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

\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]

Given:
- \( n(A \cup B) = 727 \)
- \( n(A) = 600 \)
- \( n(A \cap B) = 127 \)

We need to find \( n(B) \).

### Step 1: Substitute the known values into the formula

\[ 727 = 600 + n(B) - 127 \]

### Step 2: Simplify the equation

First, simplify the right side:

\[ 727 = 600 - 127 + n(B) \]

Calculating \( 600 - 127 \):

\[ 600 - 127 = 473 \]

So the equation becomes:

\[ 727 = 473 + n(B) \]

### Step 3: Solve for \( n(B) \)

Now, isolate \( n(B) \) by subtracting 473 from both sides:

\[ n(B) = 727 - 473 \]

Calculating \( 727 - 473 \):

\[ 727 - 473 = 254 \]

Thus, we find:

\[ n(B) = 254 \]

### Final Answer

Therefore, \( n(B) \) is equal to **254**.

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