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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&0& 1&0&1&0&0.83&1
\\\hline\textbf{2 Marks Count} &1&1&2& 0 &2&1&0&1.16&2
\\\hline\textbf{Total Marks} & 3&3&4&1&4&3&\bf{1}&\bf{3}&\bf{4}\\\hline
\end{array}}}$$

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Most answered questions in Set Theory & Algebra

1 votes
3 answers
161
Relations
Consider the set S = {a, b} and ‘L’ be a binary relation such that L = {all binary relations except reflexive relation set S}. The number of relation which are symmetric _______.
Consider the set S = {a, b} and ‘L’ be a binary relation such that L = {all binary relations except reflexive relation set S}. The number of relation which are symmet...
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1 votes
3 answers
162
Set theory doubt
Say if A is proper subset of B i.e A⊂B then is it true - that B⊆A (B is subset of A)? Also one more thing - if A⊂B then AUB = A where U means UNION
Say if A is proper subset of B i.e A⊂B then is it true - that B⊆A (B is subset of A)?Also one more thing - if A⊂B then AUB = A where U means UNION
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3 votes
3 answers
163
The gatebook
Total order relation is Lattice or not please explain?
Total order relation is Lattice or not please explain?
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24 votes
3 answers
165
GATE CSE 1987 | Question: 9b
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
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3 votes
3 answers
166
Discrete Math
How many partial functions are there from a set with m elements to a set with n elements? Q. I cannot get the intuition how the solution arrived to be (n+1)^m
How many partial functions are there from a set with m elements to a set with n elements?Q. I cannot get the intuition how the solution arrived to be (n+1)^m
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3 votes
3 answers
167
UGC NET CSE | December 2013 | Part 2 | Question: 37
Let f and g be the functions from the set of integers defined by $f(x) = 2x+3$ and $g(x) =3x+2$. Then the composition of f and g and g and f is given as 6x+7, 6x+11 6x+11, 6x+7 5x+5, 5x+5 None of the above
Let f and g be the functions from the set of integers defined by $f(x) = 2x+3$ and $g(x) =3x+2$. Then the composition of f and g and g and f is given as6x+7, 6x+116x+11, ...
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4 votes
3 answers
168
UGC NET CSE | June 2013 | Part 2 | Question: 34
The relation “devides” on a set of positive integers is_____ Symmetric and transitive Anti symmetric and transitive Symmetric only Transitive only
The relation “devides” on a set of positive integers is_____Symmetric and transitiveAnti symmetric and transitiveSymmetric onlyTransitive only
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11 votes
3 answers
169
ISRO2016-4
If $(\text{G} , .)$ is a group such that $(ab)^{-1}=a^{-1}b^{-1},\forall a,b \in \text{G},$ then $\text{G}$ is a/an Commutative semi group Abelian group Non-abelian group None of these
If $(\text{G} , .)$ is a group such that $(ab)^{-1}=a^{-1}b^{-1},\forall a,b \in \text{G},$ then $\text{G}$ is a/anCommutative semi groupAbelian groupNon-abelian groupNon...
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2 votes
3 answers
170
Lattice
How to pick an option from this I feel like both c and d are correct what do you day?
How to pick an option from this I feel like both c and d are correct what do you day?
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10 votes
3 answers
171
ISRO2007-29
The set of all Equivalence Classes of a set A of Cardinality C is of cardinality $2^c$ have the same cardinality as A forms a partition of A is of cardinality $C^2$
The set of all Equivalence Classes of a set A of Cardinality Cis of cardinality $2^c$have the same cardinality as Aforms a partition of Ais of cardinality $C^2$
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6 votes
3 answers
172
ISI2016
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
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1 votes
3 answers
176
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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4 votes
3 answers
177
TIFR-2011-Maths-A-10
Let $m \leq n$ be natural numbers. The number of injective maps from a set of cardinality m to a set of cardinality $n$ is $m!$ $n!$ $(n − m)!$ None of the above
Let $m \leq n$ be natural numbers. The number of injective maps from a set of cardinality m to a set of cardinality $n$ is $m!$$n!$ $(n − m)!$ None of the above
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2 votes
3 answers
178
The relation T is
“n/m” means that n is a factor of m, then the relation T is (a) reflexive and symmetric (b) transitive and symmetric (c) reflexive, transitive and symmetric (d) reflexive, transitive and not symmetric Ans: option (d) But how ?
“n/m” means that n is a factor of m, then the relation T is(a) reflexive and symmetric(b) transitive and symmetric(c) reflexive, transitive and symmetric(d) r...
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