If `n(u)=100,n(A)=50,n(B)=20 and n(A nnB)=10,` then `n{(AuuB)^©}`

Options

A. 60
B. 30
C. 40
D. 20

Answer

To solve the problem, we need to find \( n((A \cup B)^c) \), where \( n(U) = 100 \), \( n(A) = 50 \), \( n(B) = 20 \), and \( n(A \cap B) = 10 \).

### Step 1: Calculate \( n(A \cup B) \)

We use the formula for the union of two sets:

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

Substituting the given values:

\[ n(A \cup B) = 50 + 20 - 10 \]

Calculating this gives:

\[ n(A \cup B) = 60 \]

### Step 2: Calculate \( n((A \cup B)^c) \)

The complement of the union of sets \( A \) and \( B \) is given by:

\[ n((A \cup B)^c) = n(U) - n(A \cup B) \]

Substituting the values we have:

\[ n((A \cup B)^c) = 100 - 60 \]

Calculating this gives:

\[ n((A \cup B)^c) = 40 \]

### Final Answer

Thus, the value of \( n((A \cup B)^c) \) is \( 40 \).

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