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

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

Questions without answers in Set Theory & Algebra

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9
The number of subgroups of a cyclic group of order 12 is ______________________
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10
If [dn,/] is a lattice, then x=n/x for all x belongs to dn
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11
Can someone verify the above inferences?
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12
‘either or’ can be taken as union in discrete mathematics?
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13
why option 2 is not a distributive lattice ? i solved this and found that there are each vertex has only either one or zero complement i think it is distributive lattic...
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14
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16
why pentagon is not a lattice ?
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19
Draw the Hasse diagram for the "divides" relation (∣) on the set {0,1,…,26}
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22
Consider the partition of a set having 3 block of 5 elements each, 4 block of 2 elements each and 2 block of 3 elements in each block.Find the cardinality of equivalence ...
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25
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26
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27
Every group of prime order is always an abelian groupon this fact please explain how can a 2 element group be an abelian group, please give an example
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28
If A = {1, 3,5,7,.......}Then (A, +) is semi group or not. Doubt :a +(b+c) =( a + b) +cSo associativity property is present But a + b doesn't belong to ASo closure prop...
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29
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30
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