1. **State the problem.** We need to complete the truth table for a logic circuit. The circuit does this: - $C = A \lor B$ from an OR gate. - $D = \lnot B$ from a NOT gate. - $Q = C \oplus D$ from an XOR gate. 2. **Use the logic formulas.** - OR: $A \lor B$ is $1$ if at least one input is $1$. - NOT: $\lnot B$ flips the value of $B$. - XOR: $X \oplus Y$ is $1$ when the inputs are different, and $0$ when they are the same. 3. **Find each row one by one.** The given $A$ values are $0, 0, 1, 1$. Since the table is incomplete, the usual matching $B$ values are $0, 1, 0, 1$. 4. **Compute $C$, $D$, and $Q$ for each row.** - Row 1: $A=0$, $B=0$ - $C = A \lor B = 0 \lor 0 = 0$ - $D = \lnot B = \lnot 0 = 1$ - $Q = C \oplus D = 0 \oplus 1 = 1$ - Row 2: $A=0$, $B=1$ - $C = A \lor B = 0 \lor 1 = 1$ - $D = \lnot B = \lnot 1 = 0$ - $Q = C \oplus D = 1 \oplus 0 = 1$ - Row 3: $A=1$, $B=0$ - $C = A \lor B = 1 \lor 0 = 1$ - $D = \lnot B = \lnot 0 = 1$ - $Q = C \oplus D = 1 \oplus 1 = 0$ - Row 4: $A=1$, $B=1$ - $C = A \lor B = 1 \lor 1 = 1$ - $D = \lnot B = \lnot 1 = 0$ - $Q = C \oplus D = 1 \oplus 0 = 1$ 5. **Complete truth table.** | A | B | C | D | Q | |---|---|---|---|---| | 0 | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 1 | | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 1 | 0 | 1 | 6. **Final answer.** The completed truth table is: $$(0,0,0,1,1),\ (0,1,1,0,1),\ (1,0,1,1,0),\ (1,1,1,0,1)$$