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Syllabus: Propositional and first order logic.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1}&\textbf{2024-2}&\textbf{2023}& \textbf{2022}& \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&0&1&1& 0 & 1&1&0&0.67&1
\\\hline\textbf{2 Marks Count}&0&0&0&0 & 0&0&0&0&0
\\\hline\textbf{Total Marks}& 0&1&1& 0 & 1&1&\bf{0}&\bf{0.67}&\bf{1}\\\hline
\end{array}}}$$

Featured Questions in Mathematical Logic

#1
311
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1 answers
0 votes
Show that: (r → ~ q, r ∪ S, S → ~ q, p → q) ↔ ~ pare inconsistent.
#2
3.3k
views
4 answers
23 votes
In the following, $A$ stands for a set of apples, and $S(x, y)$ stands for "$x$ is sweeter than $y$. Let$$\Psi \equiv \exists x : x \in A$$$$\Phi \equiv \forall x \in A :...
#3
3.7k
views
3 answers
32 votes
Given that$B(x)$ means "$x$ is a bat",$F(x)$ means "$x$ is a fly", and$E(x, y)$ means "$x$ eats $y$",what is the best English translation of $$ \forall x(F(x) \rightarrow...
#4
1.6k
views
2 answers
9 votes
Match the following ListsList-IA. There are atmost two apples.B. There are exactly two apples.C. There is atmost one apple.D. There is exactly one apple.List-II1. $\foral...
#5
17.1k
views
7 answers
60 votes
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable)$((∀x)[α] ⇒ (∀x...
#6
17.1k
views
6 answers
78 votes
Which of the following predicate calculus statements is/are valid?$(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$$(\exists (x)) P(x) \w...
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