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Syllabus: Propositional and first order logic.

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

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Recent questions in Mathematical Logic

0 votes
1 answer
1041
Mathematical logic
Which of the following is(are) not logical implications? p<->q => p->q p^q => p<->q p<-> => p->~q p<->~q => p->q
Which of the following is(are) not logical implications?p<->q = p->qp^q = p<->qp<- = p->~qp<->~q = p->q
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0 votes
0 answers
1044
Limits
$\displaystyle\lim_{x \to 0} \left[ \dfrac{log(1+x)}{x} \right] ^{\dfrac{1}{x}} $
$\displaystyle\lim_{x \to 0} \left[ \dfrac{log(1+x)}{x} \right] ^{\dfrac{1}{x}} $
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0 votes
1 answer
1045
Combinatorics
Among the integers $1,2,3,....,200$ if $101$ integers are chosen,then show that there are two among the chosen,such that one is divisible by the other.
Among the integers $1,2,3,....,200$ if $101$ integers are chosen,then show that there are two among the chosen,such that one is divisible by the other.
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2 votes
2 answers
1046
Mathematical logic
[~p ^ (p->q)] - > ~p is., satisfiable unsatisfiable tautology invalid
[~p ^ (p->q)] - ~p is.,satisfiableunsatisfiabletautologyinvalid
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2 votes
2 answers
1047
Ace booklet
How many ways $4$ boys and $4$ girls can sit in a row so that no two girl are sitting side by side
How many ways $4$ boys and $4$ girls can sit in a row so that no two girl are sitting side by side
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1 votes
1 answer
1048
Combinatorics
Given m integers $a_1,a_2,....,a_m$ show that there exist integers $k,s$ with $0 \leq k < s \leq m$ such that $a_{k+1} + a_{k+2}​​​​​​ + .....+a_s$ is divisible by $m$.
Given m integers $a_1,a_2,....,a_m$ show that there exist integers $k,s$ with $0 \leq k < s \leq m$ such that$a_{k+1} + a_{k+2}​​​​​​ + .....+a_s$ is divisibl...
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0 votes
1 answer
1049
Combinatorics
Show that of any $5$ points chosen within a square of length $2$ there are $2$ whose distance apart is atmost $\sqrt{2}$.
Show that of any $5$ points chosen within a square of length $2$ there are $2$ whose distance apart is atmost $\sqrt{2}$.
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1 votes
1 answer
1051
Self doubt
In a group of five people one is either a friend or enemy of the others. It is given that no three of them are friends and no three of them are enemies. Prove that every member in that group has exactly two friends
In a group of five people one is either a friend or enemy of the others. It is given that no three of them are friends and no three of them are enemies. Prove that every ...
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0 votes
2 answers
1052
self doubt
Let $S(n)$ be the sum of the digits of positive number $n$ written in decimal notation. For example, $S(725) = = 7 + 2 + 5 = 14$. Then $X$ from $n =0$ $\displaystyle{\sum_{n=0}^{999}S(n)}$
Let $S(n)$ be the sum of the digits of positive number $n$ written in decimal notation. For example, $S(725) = = 7 + 2 + 5 = 14$. Then $X$ from $n =0$$\displaystyle{\sum...
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0 votes
1 answer
1054
Getting confused between these two
What is the difference between biconditional and logically equivalent
What is the difference between biconditional and logically equivalent
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1 answer
1056
IITK Sample written test
I Think answer should be $C$. Let , India is a stronger team than australia is $X$ and India will loose the series is $Y$ so ,$X\rightarrow Y$ can be wriiten as $Y^{'}\rightarrow X^{'}$ or $Y+X^{'}$ So answer is coming out to be $C$. Am i right?
I Think answer should be $C$.Let ,India is a stronger team than australia is $X$and India will loose the series is $Y$so ,$X\rightarrow Y$ can be wriiten as$Y^{'}\rightar...
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0 votes
1 answer
1057
ISI-MTECH-CSE-PCB-2018
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0 answers
1058
ISI-MTECH-CSE-PCB-2018
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0 votes
0 answers
1059
ISI-MTECH-CSE-PCB-2018
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0 votes
0 answers
1060
ISI-MTECH-CSE-PCB-2018
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