Question

Obtain the simple logical expression of the following. Draw the corresponding switching circuit.

[p ∨ ( ∼ q) ∨ (∼ r)] ∧ [p ∨ (q ∧ r)]

Answer 1

Using the laws of logic, we have,
[p ∨ ( ∼ q) ∨ (∼ r)] ∧ [p ∨ (q ∧ r)]
≡ [p ∨ {∼ (q ∧ r)}] ∧ [p ∨ (q ∧ r)] ......(By De Morgan’s Law)
≡ p ∨ [∼ (q ∧ r) ∧ (q ∧ r)] .........(By Distributive Law)
≡ p ∨ F ........(By Complement Law)
≡ p .............(By Identity Law)
Hence, the simple logical expression of the given expression is p.
Let p: the switch S₁ is closed
Then the corresponding switching circuit is: