JEE Main 2025 · 3 April · morning · Single correct · +4 / −1
Choose the correct logic circuit for the given truth table having inputs A and B .
| Inputs | Output | |
|---|---|---|
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
- (a)
- (b)
- (c)
- (d)
Answer and solution
Answer (a)
Solution
Physics sir · 4 steps
Read the table first: Y just copies A, so find the circuit that boils down to A alone.
- Read the table. Y is 0 whenever A = 0 and 1 whenever A = 1, whatever B is. So the target is Y = A.
- Write each output. Follow each circuit from left to right. Write down what each gate gives, then reduce the final expression.
Option Output expression Reduces to Y for AB = 00, 01, 10, 11 (a) A · (A + B) A 0, 0, 1, 1 (b) A̅ · (A + B) A̅ B 0, 1, 0, 0 (c) A · (A + B)̅ 0 0, 0, 0, 0 (d) (A + B) · B B 0, 1, 0, 1 - Why (a) works. Expand: A · (A + B) = A + AB = A(1 + B) = A, since 1 + B = 1. This is the absorption law.
- So. Only circuit (a) gives Y = A, which matches the truth table in all four rows.
The idea to keep. For a pick-the-circuit question, first spot the pattern in the truth table, then reduce each circuit with Boolean laws. Remember A(A + B) = A and A + AB = A.
Answer from the NTA final answer key. Solution by PrepWiser.