UGC-NET | UGC NET CS 2017 Jan – III | Question 60

The first order logic (FOL) statement ((R ∨ Q) ∧ (P ∨ ¬Q)) is equivalent to which of the following ?
(A) ((R ∨ ¬Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P))
(B) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P))
(C) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ ¬P))
(D) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ ( ¬R ∨ P))


Answer: (B)

Explanation: The first order logic (FOL) statement ((R ∨ Q) ∧ (P ∨ ¬Q)) is PR + ¬QR + PQ is equivalent to:

Option 1- ((R ∨ ¬Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P)) is (R + ¬Q)(P + ¬Q)(R + P))
           i.e. = RP + R¬Q +P¬Q not equivalent to  PR + ¬QR + PQ .
            2- ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P)) is (R + Q)(P + ¬Q)(P + R)
           i.e. = PR + ¬QR + PQ is exactly same.
            3- ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ ¬P)) is (R + Q)(P + ¬Q)(R + ¬P)
           i.e. = PR + ¬QR + R(P ↔ Q) not equivalent to  PR + ¬QR + PQ .
            4- ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ ( ¬R ∨ P)) is (R + Q)(P + ¬Q)(¬R + P)
           i.e. = PR + PQ + P(Q → R)  not equivalent to  PR + ¬QR + PQ.

So, option (B) is correct.


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