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Syllabus: Propositional and first order logic.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022}& \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}& 0 & 1&1&0&0&0&2&1&1&1&0&0.7&2
\\\hline\textbf{2 Marks Count}&0 & 0&0&1&1&1&1&0&0&1&0&0.5&1
\\\hline\textbf{Total Marks}& 0 & 1&1&2&2&2&4&1&1&3&\bf{0}&\bf{1.7}&\bf{4}\\\hline
\end{array}}}$$

Previous GATE Questions in Mathematical Logic

21 votes
3 answers
31
Obtain the principal (canonical) conjunctive normal form of the propositional formula $$(p \wedge q) \vee (\neg q \wedge r)$$ where $\wedge$ is logical and, $\vee$ is inc...
22 votes
3 answers
33
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$is True or False.
18 votes
3 answers
34
Show that proposition $C$ is a logical consequence of the formula$$A\wedge \left(A \to \left(B \vee C\right)\right) \wedge \left( B \to \neg A\right)$$using truth tables....
23 votes
4 answers
35
The proposition $p \wedge (\sim p \vee q)$ is:a tautologylogically equivalent to $p \wedge q$logically equivalent to $p \vee q$a contradictionnone of the above
17 votes
3 answers
36
Which of the following propositions is a tautology?$(p \vee q) \rightarrow p$$p \vee (q \rightarrow p)$$p \vee (p \rightarrow q)$$p \rightarrow (p \rightarrow q)$
55 votes
6 answers
37
39 votes
5 answers
42
What is the converse of the following assertion?I stay only if you goI stay if you goIf I stay then you goIf you do not go then I do not stayIf I do not stay then you go
52 votes
8 answers
43
What is the logical translation of the following statement?"None of my friends are perfect."$∃x(F (x)∧ ¬P(x))$$∃ x(¬ F (x)∧ P(x))$$ ∃x(¬F (x)∧¬P(x))$$ ¬�...
13 votes
3 answers
44
Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology.Let $A$ be a tautology and $B$ any other formula. Prove that $(A \ve...
43 votes
8 answers
45
34 votes
4 answers
47
32 votes
5 answers
49