GATE CS 2016 Set 2 — Question 11
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+1 / -0MediumPropositional LogicMathematical LogicEngineering MathematicsLogical Equivalence
Engineering Mathematics → Mathematical Logic → Logical Equivalence
Last updated
Question
Consider the following expressions:(i) false
(ii)
(iii) true
(iv)
(v)
The number of expressions given above that are logically implied by is
________.
(ii)
(iii) true
(iv)
(v)
The number of expressions given above that are logically implied by is
________.
Correct answer
4 to 4
Solution
The premise is .
Using the equivalence , we have:
.
Thus, the premise is true if and only if both is true and is true.We check each expression to see if it is true whenever and are both true:
(i) false: Always false. Not implied.
(ii) : True when is true. Implied.
(iii) true: Always true. Implied.
(iv) : True since is true. Implied.
(v) : Since is true, is false. Since is true, false true is true. Implied.Total number of implied expressions is 4.
Using the equivalence , we have:
.
Thus, the premise is true if and only if both is true and is true.We check each expression to see if it is true whenever and are both true:
(i) false: Always false. Not implied.
(ii) : True when is true. Implied.
(iii) true: Always true. Implied.
(iv) : True since is true. Implied.
(v) : Since is true, is false. Since is true, false true is true. Implied.Total number of implied expressions is 4.
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 Mathematical Logic
2026 Set 2 Q3A day can only be cloudy or sunny. The probability of a day being cloudy is , independent of…2026 Set 2 Q5‘When it is raining, peacocks dance.’ Based only on this sentence, which one of the following…2026 Set 2 Q8Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the…2026 Set 1 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…2026 Set 2 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…