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Question
Simplify the given circuit by writing its logical expression. Also, write your conclusion.
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Solution
Let p : The switch S1
q : The switch S2
The logical expression for the given circuit is p ∧ (~ p ∨ ~ q) ∧ q
p ∧ (~ p ∨ ~ q) ∧ q
≡ [p ∧ (~ p ∨ ~ q] ∧ q ...[Associative Law]
≡ [(p ∧ ~ p) ∨ (p ∧ ~ q)] ∧ q ...[Distributive Law]
≡ [F ∨ (p ∧ ~ q)] ∧ q ...[Complement Law]
≡ (p ∧ ~ q) ∧ q ...[Identity Law]
≡ p ∧ (~ q ∧ q) ...[Associative Law]
≡ p ∧ F ...[Complement Law]
≡ F ...[Identity Law]
Conclusion: The lamp will not glow irrespective of the status of the switches.
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