GATE CS 2021 Set 2 — Question 25
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Engineering Mathematics → Mathematical Logic → Logical Equivalence
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Question
Choose the correct choice(s) regarding the following propositional logic assertion :
Correct answer
(B) S is a tautology.; (D) The antecedent of S is logically equivalent to the consequent of S.
Solution
Let the assertion be , where:
Simplifying :
Since , the antecedent is logically equivalent to the consequent (Option D is correct).
Furthermore, the assertion is of the form
- Antecedent
- Consequent
Simplifying :
Since , the antecedent is logically equivalent to the consequent (Option D is correct).
Furthermore, the assertion is of the form
A → A, which is always true regardless of the truth values of , , and . Thus, is a tautology (Option B is correct).Continue learning with Success Tracker
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