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Syllabus: Sets, Relations, Functions, Partial orders, Lattices, Monoids, Groups.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&0&1&2&1&1&0&2&0&0&0&0.8&2
\\\hline\textbf{2 Marks Count} & 0 &2&1&0&0&1&1&0&1&2&0&0.8&2
\\\hline\textbf{Total Marks} & 1&4&3&2&1&3&2&2&2&4&\bf{1}&\bf{2.4}&\bf{4}\\\hline
\end{array}}}$$

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Recent questions in Set Theory & Algebra

3 votes
0 answers
1365
inverse function
Q. Let f be a function from A to B. Let S and T be subsets of B. Show that a) f−1(S ∪ T ) = f−1(S) ∪ f−1(T ). b) f−1(S ∩ T ) = f−1(S) ∩ f−1(T ).
Q. Let f be a function from A to B. Let S and T be subsetsof B. Show thata) f−1(S ∪ T ) = f−1(S) ∪ f−1(T ).b) f−1(S ∩ T ) = f−1(...
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1 votes
2 answers
1367
How to evaluate the given series ?
2/2(2)+3/2(3)+4/2(4) +.......
2/2(2)+3/2(3)+4/2(4) +.......
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0 votes
1 answer
1369
Lattices | hasse-diagram
Why the following Hasse Diagram is not a lattice ...?
Why the following Hasse Diagram is not a lattice ...?
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0 votes
0 answers
1372
math
explain how s2 statement is true.??
explain how s2 statement is true.??
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3 votes
4 answers
1373
Lattice
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2 votes
2 answers
1374
symmetric and antisymmetric
from definitoin of antisymmetry if aRb and bRa is present then a=b. so b should be answer,though d is right,but b is more appropriate
from definitoin of antisymmetry if aRb and bRa is present then a=b.so b should be answer,though d is right,but b is more appropriate
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0 votes
0 answers
1375
Set Theory
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0 votes
1 answer
1376
Set Theory
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1 votes
3 answers
1377
Chromatic number
What is the chromatic number of Kn - e (complete graph with an edge removed)?
What is the chromatic number of Kn - e (complete graph with an edge removed)?
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2 votes
2 answers
1378
Set Theory
How do we find whether the group is finite or infinte in questions like below ? If (G,*) is a group such that $(a * b)^{2} = (a*a) *(b*b)$ for all a,b belonging to G, then G is a) Finite group b) Infinite group c) Abelian group d) None of the above
How do we find whether the group is finite or infinte in questions like below ?If (G,*) is a group such that $(a * b)^{2} = (a*a) *(b*b)$ for all a,b belonging to G, then...
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3 votes
1 answer
1379
Set Theory
In a Group (G,*) the equation $x * a = b $ has a a) unique solution $b * a^{-1}$ b) unique solution $a^{-1} * b$ c) unique solution $a^{-1} * b^{-1}$ d) many solutions
In a Group (G,*) the equation $x * a = b $ has aa) unique solution $b * a^{-1}$b) unique solution $a^{-1} * b$c) unique solution $a^{-1} * b^{-1}$d) many solutions
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2 votes
2 answers
1380
Set Theory
The set $G = \{0,1,2,3,4,5\}$ under addition modulo 6 is a group. Which all subgroups of order 2 and 3 are possible?
The set $G = \{0,1,2,3,4,5\}$ under addition modulo 6 is a group. Which all subgroups of order 2 and 3 are possible?
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