Question

Express the following switching circuit in symbolic form of logic . Costruct its switching table and write your conlusion form it :

Answer 1

Let p : the switch `S_(1)` is closed.
q : the switch `S_(2)` is closed.
` ~p`: the switch `S_(1)` is closed or the switch `S_(1)` is open.
`~q` : the switch `S_(2)` is closed or the switch `S_(2)` is open.
From the given circuit the lamp is on if (`S_(1)` is closed) or (`S_(2)` is closed ) or (`S_(1)` is closed and `S_(2)` is closed (.
Hence , the symbolic form of the given circuit is `p vv(~q)vv(~p ^^ q)`
The switching table is :

This circuit represents a tautolgy.
Hence , the given circuit is always closed (i.e., on)