Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

Examine whether the following statement pattern is a tautology or a contradiction or a contingency. [p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)] - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]

Advertisement Remove all ads

Solution

p q r ∼ q ∼ q ∨ r p → (∼ q ∨ r) q → r p → (q → r) ∼[p → (q → r)] [p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]
T T T F T T T T F F
T T F F F F F F T F
T F T T T T T T F F
T F F T T T T T F F
F T T F T T T T F F
F T F F F T F T F F
F F T T T T T T F F
F F F T T T T T F F

All the entries in the last column of the above truth table are F.
∴ [p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)] is a contradiction.

Concept: Statement Patterns and Logical Equivalence
  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×