When both switches are open, the current will flow through the bulb and it will glow.
When switch A is closed and switch B is open, the current will flow through the bulb and it will glow.
When switch A is open and switch B is closed, the current will flow through bulb and it will glow.
When both the switches are closed, since the resistance of left arm of circuit is negligible, the current will flow through the left arm and hence the bulb will not glow.
The truth table is given as:
| A | B | Bulb |
| 0 | 0 | 1 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 1 | 0 |