Let p, q, and r be propositions and the expression (p → q) → r be a contradiction. Then, the expression (r → p) → q is
Topic-wise GATE CS PYQs with verified steps
GATE CSE 2017 Set 1 · Q29
Time
Select one answerSingle correct
Solution
Official answer: D) always TRUE when q is TRUE.
Discrete MathematicsIf the expression is a contradiction (always FALSE), then for the conditional to be FALSE:
The antecedent must be TRUE.
The consequent must be FALSE.
Now consider the expression :
Since is FALSE, the implication is vacuously TRUE regardless of the truth value of .
Substituting into the expression gives:
Thus, the expression has the same truth value as . Therefore, it is always TRUE when is TRUE.
Hence, the correct option is (D).
Try the question first, then check your work.
Examiner trap
An implication is FALSE if and only if is TRUE and is FALSE. Use the truth value of to simplify .
This Discrete Mathematics previous year question is Q29 of the GATE CSE 2017 Set 1 paper. Find more GATE CSE PYQs on Discrete Mathematics in Engineering Mathematics, or browse all GATE CSE PYQs.
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Discrete Mathematics has 50 GATE CSE PYQs across 23 papers from 2011 to 2026. 11 of them are 2-mark MCQs like this one, and GATE CSE 2017 Set 1 has 4.
How GATE tests Discrete MathematicsIndependent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.