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

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

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