Express the statement (p → q) Λ (q Λ r) in disjunctive normal form.

Question

Question

Answer 1

Answer #1

Solution :

(a) TRUTH TABLE FOR (-p1qar) r -p (qar) (-p^qr) F (b)

TRUTH TABLE FOR (-paqar) V(pa-qar)V(paqar) (paqar) (p^-qar) (paqar) (-paqar) V(pa-qar) (-paqar) V(p-qAr) (paqar) FFF TTT FTF (c)

TRUTH TABLE FOR (pAqar)V(-p^q^r) qr -p (-paqar) | (paqar) (paqar) V-paqar) F FFT TI ET TT TET T FTTT TFFF TFTF T - TT F TITIT

(d) TRUTH TABLE FOR (-pqr) V(p^-qar) -p -9 (p^q^r) (p^-qar) (-p^q^r) V(p^-qar) FFTT . FTTT FTFTF FTTTFI TFFFT TFT FT 1 TT TT - TT

from above tables we can observe that first table and option - (c) are identical.

∴ (p→q)∧(q∧r) = (p∧q∧r)∨(¬p∧q∧r)

∴ option - (c) is correct

Answer 2

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​Express the statement (p → q) Λ (q Λ r) in disjunctive normal form.