The First Order Logic (FOL) statement (R∨Q)∧(P∨¬Q) is equivalent to which of…

Given:

(R ∨ Q) ∧ (P ∨ ¬Q)

Using Boolean algebra:

(R + Q)(P + Q̅)

Expanding,

= RP + RQ̅ + PQ + QQ̅

Since,

QQ̅ = 0

therefore,

= RP + RQ̅ + PQ

Now check Option B:

(R + Q)(P + Q̅)(R + P)

First compute:

(R + Q)(P + Q̅)

= RP + RQ̅ + PQ

Now multiply by (R + P):

(RP + RQ̅ + PQ)(R + P)

Using absorption laws:

RP(R + P) = RP

RQ̅(R + P) = RQ̅

PQ(R + P) = PQ

Hence,

= RP + RQ̅ + PQ

which is exactly the original expression.

Therefore,

(R ∨ Q) ∧ (P ∨ ¬Q)

≡ (R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P)

Correct Option: B