GATE CS 2026 Set 2 — Question 5
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33EasyPropositional LogicMathematical LogicEngineering MathematicsDeduction & InductionAnalytical AptitudeGeneral Aptitude
Engineering Mathematics → Analytical Aptitude → Deduction & Induction
Last updated
Question
‘When it is raining, peacocks dance.’Based only on this sentence, which one of the following options is necessarily true?
Correct answer
(C) When peacocks are not dancing, it is not raining.
Solution
The given statement is a conditional statement of the form "If , then " (), where:
: It is raining
: Peacocks danceThe statement is: .Let's analyze the options:
(A) "Peacocks dance only when it is raining" implies that if peacocks are dancing, it must be raining (). This is the converse, which is not necessarily true.
(B) "When peacocks dance, it is raining" is also . This is the converse, not necessarily true.
(C) "When peacocks are not dancing, it is not raining" translates to "If not , then not " (). This is the contrapositive of the original statement. In logic, a conditional statement is always logically equivalent to its contrapositive. Therefore, this must be true.
(D) "When it is not raining, peacocks do not dance" translates to "If not , then not " (). This is the inverse, which is not necessarily true.Thus, option (C) is the correct answer.
: It is raining
: Peacocks danceThe statement is: .Let's analyze the options:
(A) "Peacocks dance only when it is raining" implies that if peacocks are dancing, it must be raining (). This is the converse, which is not necessarily true.
(B) "When peacocks dance, it is raining" is also . This is the converse, not necessarily true.
(C) "When peacocks are not dancing, it is not raining" translates to "If not , then not " (). This is the contrapositive of the original statement. In logic, a conditional statement is always logically equivalent to its contrapositive. Therefore, this must be true.
(D) "When it is not raining, peacocks do not dance" translates to "If not , then not " (). This is the inverse, which is not necessarily true.Thus, option (C) is the correct answer.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Analytical Aptitude
2026 Set 1 Q1The antonym of the word protagonist is ________.2026 Set 2 Q1Expedite, Hasten, Hurry, __________ Fill the blank by choosing a word with a meaning similar to…2026 Set 1 Q2The figure shows two 4-tile patterns. [figure] Either one or both of the patterns can be used any…2026 Set 2 Q2A black square PQRS has been cut into two parts. One part of it is shown in Panel I. Which one of…2026 Set 1 Q3Consider a knock-out women’s badminton singles tournament where there are no ties. The loser in…