ISRO CS 2025 Q.59: solution and answer

ISRO 2025 · CSQ.59 · 1 mark · MCQ

Let the scenario 'If the vehicle is powered ON and if power is available to the avionics package, then communication to the vehicle will be established' be represented with statements
p = power is available to avionics package;
q = vehicle is powered ON;
r = communication to the vehicle will be established.
The logic form $(p \land q) \to r$ is equivalent to

(A)
$\neg r \to (p \land q)$
(B)
$p \to (q \land r)$
(C)
$\neg p \lor \neg q \lor r$
(D)
None of the above

See the question in the paper

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Answer and solution

ANSWER

The correct option is (C): $\neg p \lor \neg q \lor r$ .

Official answer: CSource: ISRO's final answer key of 15 May 2026

An implication $a \to b$ is equivalent to $\neg a \lor b$ . So $(p \land q) \to r \equiv \neg (p \land q) \lor r$ .
By De Morgan's law, $\neg (p \land q) \equiv \neg p \lor \neg q$ .
Hence $(p \land q) \to r \equiv \neg p \lor \neg q \lor r$ , which is option (c).
Option (a): $\neg r \to (p \land q) \equiv r \lor (p \land q)$ . Take $p = q = r = F$ . The original statement is true, because its antecedent is false. Option (a) is false. They are not equivalent.
Option (b): $p \to (q \land r) \equiv \neg p \lor (q \land r)$ . Take $p = T, q = F, r = T$ . The original statement is true, because its antecedent is false. Option (b) is false, because $\neg p$ is false and $q \land r$ is false. They are not equivalent.
Option (c) is equivalent to the given form, so (d) is wrong.

KEY IDEA

Rewrite the implication as a disjunction, $a \to b \equiv \neg a \lor b$ , then push the negation through the conjunction with De Morgan's law.

WATCH OUT FOR

Confusing an implication with its converse or with a different grouping, such as $p \to (q \land r)$ . Only the contrapositive $\neg r \to \neg (p \land q)$ is equivalent to the original, not $\neg r \to (p \land q)$ .

From the ISRO CS 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 2 ISRO Logic questions, with notes