A B
0 0 Switch 1 wired permanently closed
0 1 OR gate connected to A and B with
output to switch 2, switches 1 and 2 now closed
1 0 Switch 1 on, Switch 2 on through OR gate
Switch 3 connected to A. Switches 1, 2 and 3 now closed
1 1 AND gate connected to A and B with
output to switch 4. Switch 1 on, switch
2 on through OR gate, switch 3 on
through connection to A, switch 4 on
through AND gate.
So, you can do this with one OR gate and one AND gate, available in a single 74HC58 IC, isn't Boolean Logic fun!
Edit: Added 74HC58 information