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Syllabus: Propositional and first order logic.

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

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Highest voted questions in Mathematical Logic

2 votes
2 answers
571
GATE [Math]
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2 votes
1 answer
573
Quiz Question
Which of the following interference system is invalid? $R \rightarrow S, \sim \vdash \sim R$ $\sim R, P \rightarrow Q, Q \rightarrow R \vdash \sim P$ ... Iam getting answer as c but given b.
Which of the following interference system is invalid?​​$R \rightarrow S, \sim \vdash \sim R$$\sim R, P \rightarrow Q, Q \rightarrow R \vdash \sim P$$\sim R \rightar...
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2 votes
1 answer
574
Group theory
Let the number of non-isomorphic groups of order 10 be X and number of non-isomorphic groups of order 24 be Y then the value of X and Y a) 3,2 b)2,7 c)1,7 d)4,5
Let the number of non-isomorphic groups of order 10 be X and number of non-isomorphic groups of order 24 be Y then the value of X and Ya) 3,2b)2,7c)1,7d)4,5
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2 votes
1 answer
575
Group theory
Let $G$ be a group whose presentation is $G=\{ x, y \mid x^5 =y^2 =e, \:\:\:\: x^2y=yx\}$, $\mathcal{Z}_n$: Set of integers modulo $n$ Then $G$ is isomorphic to $\mathcal{Z}_5$ $\mathcal{Z}_{10}$ $\mathcal{Z}_2$ $\mathcal{Z}_{30}$
Let $G$ be a group whose presentation is$G=\{ x, y \mid x^5 =y^2 =e, \:\:\:\: x^2y=yx\}$,$\mathcal{Z}_n$: Set of integers modulo $n$Then $G$ is isomorphic to$\mathcal{Z}_...
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2 votes
1 answer
576
predicate
B(x):x is a boy C(x):x is a chocolates E(x,y): x eats y. "only boy eats chocolates". write this statement using predicate calculus.
B(x):x is a boyC(x):x is a chocolatesE(x,y): x eats y."only boy eats chocolates". write this statement using predicate calculus.
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2 votes
3 answers
577
Rosen chapter 5.5 question 50
How many ways are there to distribute 5 distinguishable objects into three indistinguishable boxes?
How many ways are there to distribute 5 distinguishable objects into three indistinguishable boxes?
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2 votes
3 answers
580
UGC NET CSE | December 2014 | Part 3 | Question: 57
The resolvent of the set of clauses $(A \vee B, \sim A \vee D, C \vee \sim B)$ is $A \vee​ B$ $C \vee​ D$ $A \vee​ C$ $A \vee​ D$
The resolvent of the set of clauses $(A \vee B, \sim A \vee D, C \vee \sim B)$ is $A \vee​ B$$C \vee​ D$$A \vee​ C$$A \vee​ D$
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2 votes
1 answer
582
UGC NET CSE | September 2013 | Part 2 | Question: 24
The quantification $\exists ! x P(x)$ ... $\exists x P(x) \wedge \forall x \forall y ((P(x) \vee P(y)) \rightarrow x=y)$
The quantification $\exists ! x P(x)$ denotes the proposition “There exists a unique x such that P(x) is true”, express he quantification using universal and existent...
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2 votes
1 answer
584
IISC-CSA-Research-Test-8
Write the truth table for the connective: "If A then B"
Write the truth table for the connective: "If A then B"
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2 votes
2 answers
588
Logically Equivalent justify your answer
1. (∀x (p(x) → q(x)) and (∀x p(x) → ∀x q(x)) 2.∃x p(x)∧∃x q(x) and ∃x (p(x)∧q(x)) 3.(∀x (p(x) ↔ q(x)) and (∀x p(x) ↔ ∀x q(x)) are logically equivalent or not justify the answer
1. (∀x (p(x) → q(x)) and (∀x p(x) → ∀x q(x))2.∃x p(x)∧∃x q(x) and ∃x (p(x)∧q(x))3.(∀x (p(x) ↔ q(x)) and (∀x p(x) ↔ ∀x q(x))are logically eq...
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2 votes
1 answer
589
LOGIC BASIC
how would you represent that statement into logical from : if the directory DB is opened then monitor is put in a closed state , if the system is not in initial state ?
how would you represent that statement into logical from : if the directory DB is opened then monitor is put in a closed state , if the system is not in initial state ?
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2 votes
2 answers
590
Conditional Statements is a tautology or not without using truth table
1.$ [(p\to q)\wedge (q\to r)]\to (p\to r)$ 2. $[(p \vee q) \wedge (p \to r) \wedge (q \to r)] \to r$
1.$ [(p\to q)\wedge (q\to r)]\to (p\to r)$2. $[(p \vee q) \wedge (p \to r) \wedge (q \to r)] \to r$
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