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

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following: [∼ p ∧ (∼ q ∧ r)] ∨ [(q ∧ r) ∨ (p ∧ r)] - Mathematics and Statistics

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

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

[∼ p ∧ (∼ q ∧ r)] ∨ [(q ∧ r) ∨ (p ∧ r)]

Advertisement Remove all ads

Solution

Truth values of p and q are T and truth values of r and s are F.

[∼ p ∧ (∼ q ∧ r)] ∨ [(q ∧ r) ∨ (p ∧ r)]
≡ [∼ T ∧ (∼ T ∧ F)] ∨ [(T ∧ F) ∨ (T ∧ F)]
≡ [F ∧ (F ∧ F)] ∨ [F ∨ F]
≡ (F ∧ F) ∨ F
≡ F ∨ F ≡ F
Hence the truth value of the given statement is false.

Concept: Truth Value of Statement
  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×