Propositional and First-Order Logic: GATE CS previous year questions (Engineering Mathematics)

GATE CS 2026 Set 2MCQ1 markEasy (estimate)
GATE CS 2026 Set 2, Q.11
For two different persons $x$ and $y$ , the predicate $M (x, y)$ denotes that $x$ knows $y$ . Consider the following statement. There is a person who does not know anyone else, but...
Propositional and First-Order Logic
GATE CS 2025 Set 1MSQ2 marksMedium (estimate)
GATE CS 2025 Set 1, Q.48
Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"? The meanings of the predicates used...
Propositional and First-Order Logic
GATE CS 2025 Set 2MCQ1 markEasy (estimate)
GATE CS 2025 Set 2, Q.15
Let $P (x)$ be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?
Propositional and First-Order Logic · Combinatorics, Counting, Recurrence Relations and Generating Functions
GATE CS 2024 Set 2MCQ1 markEasy (estimate)
GATE CS 2024 Set 2, Q.12
Let $p$ and $q$ be the following propositions: $p$ : Fail grade can be given. $q$ : Student scores more than 50% marks. Consider the statement: "Fail grade cannot be given when st...
Propositional and First-Order Logic
GATE CS 2023MSQ1 markMedium (estimate)
GATE CS 2023, Q.26
Geetha has a conjecture about integers, which is of the form $\forall x (P (x) ⟹ \exists y Q (x, y)),$ where $P$ is a statement about integers, and $Q$ is a statement abo...
Propositional and First-Order Logic
GATE CS 2021 Set 1MCQ1 markEasy (estimate)
GATE CS 2021 Set 1, Q.17 (CS Q.7)
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_{1} : (\neg p \land (p \lor q)) \to q$ …
Propositional and First-Order Logic
GATE CS 2021 Set 2MSQ1 markEasy (estimate)
GATE CS 2021 Set 2, Q.25 (CS Q.15)
Choose the correct choice(s) regarding the following propositional logic assertion $S$ : $S : ((P \land Q) \to R) \to ((P \land Q) \to (Q \to R))$
Propositional and First-Order Logic
GATE CS 2020MCQ2 marksMedium (estimate)
GATE CS 2020, Q.49 (CS Q.39)
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$ .
Propositional and First-Order Logic
GATE CS 2019MCQ2 marksMedium (estimate)
GATE CS 2019, Q.45 (CS Q.35)
Consider the first order predicate formula $φ$ …
Propositional and First-Order Logic
GATE CS 2018MCQ2 marksMedium (estimate)
GATE CS 2018, Q.38 (CS Q.28)
Consider the first-order logic sentence $φ \equiv \exists s \exists t \exists u \forall v \forall w \forall x \forall y ψ (s, t, u, v, w, x, y)$ where…
Propositional and First-Order Logic
GATE CS 2017 Set 1MCQ1 markEasy (estimate)
GATE CS 2017 Set 1, Q.1 (CS Q.1)
The statement $(\neg p) ⟹ (\neg q)$ is logically equivalent to which of the statements below? I. $p ⟹ q$ II. $q ⟹ p$ III. $(\neg q) \lor p$ IV.…
Propositional and First-Order Logic
GATE CS 2017 Set 1MCQ1 markMedium (estimate)
GATE CS 2017 Set 1, Q.2 (CS Q.2)
Consider the first-order logic sentence $F : \forall x (\exists y R (x, y))$ . Assuming non-empty logical domains, which of the sentences below are implied by $F$ ? I.…
Propositional and First-Order Logic
GATE CS 2017 Set 1MCQ2 marksMedium (estimate)
GATE CS 2017 Set 1, Q.29 (CS Q.29)
Let $p, q$ , and $r$ be propositions and the expression $(p \to q) \to r$ be a contradiction. Then, the expression $(r \lor p) \to q$ is
Propositional and First-Order Logic
GATE CS 2017 Set 2MCQ1 markEasy (estimate)
GATE CS 2017 Set 2, Q.11 (CS Q.11)
Let $p, q, r$ denote the statements “It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleasant, and it is not pl...
Propositional and First-Order Logic
GATE CS 2016 Set 1NAT1 markMedium (estimate)
GATE CS 2016 Set 1, Q.11 (CS Q.1)
Let $p, q, r, s$ represent the following propositions. $p : x \in {8, 9, 10, 11, 12}$ $q : x$ is a composite number $r : x$ is a perfect square $s : x$ is a prime number The integ...
Propositional and First-Order Logic
GATE CS 2016 Set 2NAT1 markMedium (estimate)
GATE CS 2016 Set 2, Q.11 (CS Q.1)
Consider the following expressions: (i) $false$ (ii) $Q$ (iii) $true$ (iv) $P \lor Q$ (v) $\neg Q \lor P$ The number of expressions given above that are logically...
Propositional and First-Order Logic
GATE CS 2016 Set 2MCQ2 marksMedium (estimate)
GATE CS 2016 Set 2, Q.37 (CS Q.27)
Which one of the following well-formed formulae in predicate calculus is NOT valid?
Propositional and First-Order Logic
GATE CS 2015 Set 1MCQ1 markEasy (estimate)
GATE CS 2015 Set 1, Q.24 (CS Q.14)
Which one of the following is NOT equivalent to $p \leftrightarrow q$ ?
Propositional and First-Order Logic
GATE CS 2015 Set 2MCQ1 markEasy (estimate)
GATE CS 2015 Set 2, Q.13 (CS Q.3)
Consider the following two statements. $S_{1}$ : If a candidate is known to be corrupt, then he will not be elected. $S_{2}$ : If a candidate is kind, he will be elected. Which one of...
Propositional and First-Order Logic
GATE CS 2015 Set 2MCQ2 marksEasy (estimate)
GATE CS 2015 Set 2, Q.65 (CS Q.55)
Which one of the following well formed formulae is a tautology?
Propositional and First-Order Logic
GATE CS 2015 Set 3MCQ1 markMedium (estimate)
GATE CS 2015 Set 3, Q.34 (CS Q.24)
In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in tha...
Propositional and First-Order Logic
GATE CS 2014 Set 1MCQ1 markEasy (estimate)
GATE CS 2014 Set 1, Q.11 (CS Q.1)
Consider the statement $“Not all that glitters is gold”$ Predicate $g l i tt er s (x)$ is true if $x$ glitters and predicate $g o l d (x)$ is true if $x$ is gold. Which one of th...
Propositional and First-Order Logic
GATE CS 2014 Set 1MCQ2 marksEasy (estimate)
GATE CS 2014 Set 1, Q.63 (CS Q.53)
Which one of the following propositional logic formulas is TRUE when exactly two of $p$ , $q$ , and $r$ are TRUE?
Propositional and First-Order Logic
GATE CS 2014 Set 2MCQ2 marksEasy (estimate)
GATE CS 2014 Set 2, Q.63 (CS Q.53)
Which one of the following Boolean expressions is NOT a tautology?
Propositional and First-Order Logic
GATE CS 2014 Set 3MCQ1 markEasy (estimate)
GATE CS 2014 Set 3, Q.11 (CS Q.1)
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the...
Propositional and First-Order Logic
GATE CS 2014 Set 3MCQ2 marksEasy (estimate)
GATE CS 2014 Set 3, Q.63 (CS Q.53)
The CORRECT formula for the sentence, "not all rainy days are cold" is
Propositional and First-Order Logic
GATE CS 2013MCQ2 marksEasy (estimate)
GATE CS 2013, Q.27 (CS Q.27)
What is the logical translation of the following statement? "None of my friends are perfect."
Propositional and First-Order Logic
GATE CS 2013MCQ2 marksMedium (estimate)
GATE CS 2013, Q.47 (CS Q.47)
Which one of the following is NOT logically equivalent to $\neg\exists x (\forall y (α) \land \forall z (β))$ ?
Propositional and First-Order Logic
GATE CS 2012MCQ1 markEasy (estimate)
GATE CS 2012, Q.1 (CS Q.1)
Consider the following logical inferences. $I_{1}$ : If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. $I_{2}$ : If it...
Propositional and First-Order Logic
GATE CS 2012MCQ1 markEasy (estimate)
GATE CS 2012, Q.13 (CS Q.13)
What is the correct translation of the following statement into mathematical logic? "Some real numbers are rational"
Propositional and First-Order Logic
GATE CS 2011MCQ2 marksEasy (estimate)
GATE CS 2011, Q.30 (CS Q.30)
Which one of the following options is CORRECT given three positive integers $x$ , $y$ and $z$ , and a predicate…
Propositional and First-Order Logic

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