Question

Find the alternative arrangement using minimum switches for the following switching circuit.

Answer 1

The symbolic form is

p ∧ [q ∨ {r ∧ (∼p ∨ (∼ q ∧ p)}]

= p ∧ [q ∨ {r ∧ ((∼p ∨∼ q) ∧ (∼ p ∨ p)]   ....(Distributive law)

= p ∧ [q ∨ {r ∧ (∼p v ∼ q) ∧ T}]   ....(Complement law)

= p ∧ [q ∨ {r ∧ (∼p ∨∼ q)}]   ....(Identity law)

= p ∧ [(q ∨ r) ∧ (q ∨ (∼p ∨ ∼ q))]   ....(Distributive law)

= p ∧ [(q ∨ r) ∧ {(q ∨∼ q) ∨ ∼ p}]  ....(Assocative law)

= p ∧ [(q ∨ r) ∧ {T ∨ ∼ p}]   ....(Complement law)

= p ∧ [(q ∨ r) ∧ T]   ....(Identity law)

= p ∧ (q ∨ r)   ....(Identity law)

∴ Alternative arrangement is