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Question:

Consider the following three statements: P: 5 is a prime number. Q: 7 is a factor of 192. R: L.C.M. of 5 and 7 is 35. Then the truth value of which one of the following statements is true?

(P∧Q)∨(¬R)

(¬P)∨(Q∧R)

P∨(¬Q∧R)

(¬P)∧(¬Q∧R)

Solution:

P is True
Q is False
R is True
Option 4) ¬P∧(¬Q∧R) = F∧(T∧T) = F∧T = F
Option 1) (P∧Q)∨(¬R) = (T∧F)∨F = F∨F = F
Option 2) (¬P)∨(Q∧R) = F∨(F∧T) = F∨F = F
Option 3) P∨(¬Q∧R) = T∨(T∧T) = T∨T = T
Therefore, the truth value of P∨(¬Q∧R) is true.