Simplify the Boolean expression (P ∧ Q ∧ ~R) ∨ (~P ∧ Q ∧ R) ∨...

Question

Question

Simplify the Boolean expression

(P ∧ Q ∧ ~R) ∨ (~P ∧ Q ∧ R) ∨ (~P ∧ ~Q ∧ R)

could you also list the laws you used?

engineering Computer-Science

Answer 1

Answer #1

(P ∧ Q ∧ ~R) ∨ (~P ∧ Q ∧ R) ∨ (~P ∧ ~Q ∧ R)

= (P ∧ Q ∧ ~R)∨((~P ∧ Q ∧ R) ∨ (~P ∧ ~Q ∧ R)) [ Associative law]

=(P ∧ Q ∧ ~R)∨(~P∧ R(Q∨~Q))

=(P ∧ Q ∧ ~R)∨(~P∧ R) [ Q∨~Q = True & A .True = A] [simplified form]

Answer 2

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