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

Using the truth table prove the following logical equivalence. (p ∨ q) → r ≡ (p → r) ∧ (q → r) - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Chart

Using the truth table prove the following logical equivalence.

(p ∨ q) → r ≡ (p → r) ∧ (q → r)

Advertisement Remove all ads

Solution

1 2 3 4 5 6 7 8
p q r p ∨ q (p ∨ q) → r p → r q → r (p → r) ∧ (q → r)
T T T T T T T T
T T F T F F F F
T F T T T T T T
T F F T F F T F
F T T T T T T T
F T F T F T F F
F F T F T T T T
F F F F T T T T

The entries in columns 5 and 8 are identical.
∴ (p ∨ q) → r ≡ (p → r) ∧ (q → r)

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×