Use laws of logical equivalence to simplify the circuit. Justify each step. ((𝑃 ∧ ~𝑄) ∨ (𝑃 ∧ 𝑄)) ∧ Q

Question

Use laws of logical equivalence to simplify the circuit. Justify each step. ((𝑃 ∧ ~𝑄) ∨ (𝑃 ∧ 𝑄)) ∧ Q

Answer 1

P and (P and Q) and ~q or (P and Q) and Q

By associative and commutative property of AND:

[( P and Q and ~q) and (P and Q)] or (P and Q)

Q and ~Q is false, so the entire first term

inside the square brackets is false

the truth value therefore depends entirely of P and Q