If `A=B=C=1 and X= bar(ABC)+Bbar(CA)+Bbar(CA)+Cbar(AB)`, then X=

Options

A. 0
B. 1
C. 100
D. 110

Explanation

To solve the expression \( X = \overline{ABC} + \overline{B}(CA) + \overline{B}(CA) + \overline{C}(AB) \) given \( A = B = C = 1 \), we will follow these steps:

### Step 1: Substitute the values of A, B, and C
Since \( A = 1 \), \( B = 1 \), and \( C = 1 \), we can substitute these values into the expression for \( X \).

\[ X = \overline{(1)(1)(1)} + \overline{(1)}(1 \cdot 1) + \overline{(1)}(1 \cdot 1) + \overline{(1)}(1 \cdot 1) \]

### Step 2: Calculate the complements
Now we calculate the complements:
- \( \overline{(1)(1)(1)} = \overline{1} = 0 \)
- \( \overline{(1)} = 0 \)

Substituting these values into the expression gives:

\[ X = 0 + 0(1) + 0(1) + 0(1) \]

### Step 3: Simplify the expression
Now, we simplify the expression:

\[ X = 0 + 0 + 0 + 0 = 0 \]

### Final Answer
Thus, the value of \( X \) is \( 0 \).

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