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

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

Recent questions in Set Theory & Algebra

#201
291
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Does associative properties follows only when all the operators in the given expression same (union or intersection) or it do follows when there are different symbols present in the given expression.E.g ... b) /\ c U d = a U (b /\ c) U d.
#202
824
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1 answers
0 votes
I know that the number of equivalence relation is bell no. i.e 7th bell no. i.e. 877, but i am not able to find the cardinality of R!Please help!
#203
799
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1 answers
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I am struggling to find complement of ‘b’ clearly ‘c’ and ‘d’ are not, also ‘g’ can also not be complement since (g join b = g).Please help me with this!
#204
382
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TRUE/FALSE?(1) If * is any binary operation on any set S then a * a = a for all a∈S.(2) If * is any commutative binary operation on any set S, then a* ... a set S may assign more than one element of S to each ordered pair of elements of S.
#205
8.0k
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2 answers
14 votes
Which of the following statements is/are $\text{TRUE}$ for a group $\textit{G}?$ ... .If $\textit{G}$ is commutative, then a subgroup of $\textit{G}$ need not be commutative.
#206
461
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1 answers
0 votes
Let A={2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} and consider the divides relation on A. Let C denote the length of the maximal chain, M the number of maximal element, and m the number ... is true?C=3,M=8,m=6C=4,M=8,m=6C=3,M=6,m=6C=4,M=6,m=4
#207
2.2k
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2 answers
0 votes
A newspaper agent sells the TOI, the HT and the IN in equal numbers to 302 persons. 7 persons get the HT and the IN, 12 get the TOI and the IN, 9 get ... 3 get all three newspapers. Then the number of persons who get only one paper is ____
#208
609
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0 votes
#209
337
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1 answers
0 votes
The number of all abelian groups, up to isomorphism, of order 32 is not:4567
#210
792
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0 votes
Let G be a group of 52 elements. The largest possible size of a subgroup of G other than G itself is ____.
#211
737
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1 answers
0 votes
Consider the following statements S1 and S2 : S1 :The minimal elements of a poset always form an antichain. S2 : The maximal elements of a poset always ... of the following is correct?Can someone explain these two with examples? Thank you!
#212
262
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0 answers
0 votes
#213
417
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1 answers
0 votes
Let $C(n,r)= \binom{n}{r}$.The value of $\sum_{k=0}^{20}(2k+1)C(41,2k+1)$ is :A)40(2)^40 B)40(2)^39C)41(2)^40D)41(2)^39
#214
338
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1 answers
0 votes
Sir, kindly solve this.
#215
222
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1 answers
0 votes
Using DeMorgan's rule, state the negation of the statement: The car is out of gas or the fuel line is plugged. (a) The car has gas or the fuel line is ... the fuel line is plugged(d) The car is out of gas or the fuel line is plugged
#216
421
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1 answers
0 votes
Given p, we want to prove q. Which of the following will suffice:(a) ¬q =⇒ ¬p(b) p ∧ q =⇒ q(c) ¬p ∧ ¬q =⇒ p(d) ¬q =⇒ q(e) p ∧ ¬q ∧ r =⇒ ¬r(f) none of these
#217
385
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1 answers
2 votes
The sum $\displaystyle{}\sum_{k=1}^{n}(1 + 2 + \dots + k)$ is a polynomial of what degree$1$2$3$4$5$
#218
327
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0 answers
0 votes
Let P(n) be a statement and we prove P(k) ⇒ $P(k^{2})$ and P(k) ⇒ P(k + 3). Then we to prove that P(n) is true for all n (a) it is enough to prove ... that base case for k = 1 and k = 2 and k = 3(d) No base case can prove the statement.
#219
202
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0 answers
0 votes
Let P(n) be a statement and we prove P(k) ⇒ P(k − 3) and P(k) ⇒ P(2k). Then we to prove that P(n) is true for all n (a) it is enough to prove the base ... that base case for k = 1 and k = 2 and k = 3(d) No base case can prove the statement
#220
260
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1 answers
0 votes
Do we have multigraph concepts in GATE 2022?? Pls help me out!