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

(1) ((R ∨ ¬Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P))

(2) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ P))

(3) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (R ∨ ¬P))

(4) ((R ∨ Q) ∧ (P ∨ ¬Q) ∧ (¬R ∨ P))
asked in Mathematical Logic by Loyal (3.2k points) 4 41 | 33 views

1 Answer

+1 vote

i can write this like:

    (R+Q) (P+~Q)

    =RP+R~Q+PQ

now option (c)

   (R+Q) (P+~Q) (R+~P)

=(RP+R~Q+QP) (R+~P)

=RP+R~Q+PQR+~P~QR+QP

=RP+~QR(1+~P)+PQ(1+R)

=RP+~QR+PQ

SO OPTION(3) WILL BE ANSWER

answered ago by Junior (521 points) 6


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