Question
Check whether the following switching circuits are logically equivalent – Justify.
✓
Answer
Let $p$ : the switch $S_1$ is closed
$q$ : the switch $S_2$ is closed
$r$ : the switch $S_3$ is closed
(A) The symbolic form of the given switching circuits are
$p ∧ (q ∨ r)$ and $(p ∧ q) ∨ (p ∧ r)$ respectively.
By Distributive Law, $p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)$
Hence, the given switching circuits are logically equivalent.
$q$ : the switch $S_2$ is closed
$r$ : the switch $S_3$ is closed
(A) The symbolic form of the given switching circuits are
$p ∧ (q ∨ r)$ and $(p ∧ q) ∨ (p ∧ r)$ respectively.
By Distributive Law, $p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)$
Hence, the given switching circuits are logically equivalent.
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