Engineering
Mathematics
Logical Operator Reasoning AND and OR
Algebra of Statements
Logical Operator Reasoning Conditional and Bi Conditional
Question
Which one of the following statements is not a tautology?
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Solution
(A) (p ∨ q) → (p ∨ (~ q))
= ~ (p ∨ q) ∨ (p ∨ ~ q)
= (~ p ∧ ~ q) ∨ (p ∨ ~ q)
≠ T
(B) (p ∧ q) → p
=~ (p ∧ q) ∨ p = (~ p ∨ ~ q) ∨ p
= (~ p ∨ p) ∨ ~ q
= T
(C) ~ p ∨ (p ∨ q)
= (~ p ∨ p) ∨ q = T
(D) ~ (p ∨ q) ∨ (~ p ∨ q)
= (~ p ∨ ~ q) ∨ (~ p ∨ q)
= ~ p ∨ T = T