GATE CS 2014 Set 2 — Question 63
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Engineering Mathematics → Mathematical Logic → Propositional Logic
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Question
Which one of the following Boolean expressions is NOT a tautology?
Correct answer
(B) (a rightarrow c) → (b → (a ∧ c))
Solution
We check each option:(A) is the Law of Syllogism (Transitivity of Implication). It is a tautology.(B)
Let .
Then is True.
is True.
is False.
So, is
The entire expression becomes
Since there is a case where it is False, it is NOT a tautology.(C)
If LHS is True, then are all True. Then RHS is True.
Let .
Then is True.
is True.
is False.
So, is
T → F, which is False.The entire expression becomes
T → F, which is False.Since there is a case where it is False, it is NOT a tautology.(C)
If LHS is True, then are all True. Then RHS is True.
T → T is True. If LHS is False, the implication is True. Thus, it is a tautology.(D) . It is a tautology.Continue learning with Success Tracker
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