GATE DA 2025 Set 1 — Question 15
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Artificial Intelligence → Propositional Logic → Logical Equivalence
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Question
Let and be any two propositions. Consider the following propositional statements.
where denotes conjunction (AND operation), denotes disjunction (OR operation), and denotes negation (NOT operation). Which one of the following options is correct?
(Note: denotes logical equivalence)
where denotes conjunction (AND operation), denotes disjunction (OR operation), and denotes negation (NOT operation). Which one of the following options is correct?
(Note: denotes logical equivalence)
Correct answer
(A) S₁ ≡ S₃
Solution
To determine which statements are logically equivalent, we analyze each one:
1.: The logical implication is defined as being true in all cases except when is true and is false. This is logically equivalent to .
2.: This represents the case where is false AND is true.
3.: This represents the case where is false OR is true.
4.: By De Morgan's Law, this is equivalent to .
Comparing the statements:Continue learning with Success Tracker
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