A long corridor has a single light bulb and two doors with light switch at each door. Design logic circuit for the light; assume that the light is off when both switches are
in the same position

The answer is below

Explanation:

Let A represent the first switch, B represent the second switch and C represent the bulb. Also, let 0 mean  turned off and 1 mean turned on. Since when both switches are  in the same position, the light is off. This can be represented by the following truth table:

A                    B                       C (output)

0                    0                        0

0                    1                          1

1                     0                         1

1                     1                          0

The logic circuit can be represented by:

C = A'B + AB'

The output (bulb) is on if the switches are at different positions; if the switches are at the same position, the output (bulb) is off. This is an XOR gate. The gate is represented in the diagram attached below.