Which one of the following Boolean expressions is NOT a tautology?
2017
Which one of the following Boolean expressions is NOT a tautology?
- A.
((a → b) ∧ (b → c)) → (a → c)
- B.
(a ↔ c) →( ¬b → (a ∧ c))
- C.
(a ∧ b ∧ c) → (c ∨ a)
- D.
a → (b → a)
Attempted by 39 students.
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Correct answer: B
A tautology is a Boolean expression that evaluates to True for all possible truth values of its variables. Option 0 represents the Law of Syllogism, which is a standard tautology. Options 2 and 3 are also known logical forms that always evaluate to True. Option 1 is not a tautology because it can be False under certain conditions. For example, if a = False, b = False, and c = False, the expression evaluates to False. Therefore, Option 1 is the correct answer.
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