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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

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Is this monoid:Addition modulo (take mode using m) on the set of Integers (Z m)={0,1,2,3,4,…..m-1}i.e. For all a a (+ modulo using m) e = e (+ modulo using m) a =a here, e is an identity element
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#583
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Consider the group (G,*) where G is real number system except 1 and * is defined as a*b=a+b-ab then the inverse of -2 in this group is ________.
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given a relation on R on the set A={1,2,3,4} in the form of matrix representation as ,$M_R$ ... Then the cardinality of the smallest equivalence relation on A which contains R is equal toanswer given-16
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#586
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#588
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A 12B 8C 13D 16
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CONSIDER A WOSET (WELL ORDERED SET) (Z+ * Z+ ,<=) WHICH IS DEFINED AS POSET + COMPARABILITY + LEAST ELEMENTWHAT IS THE LEAST ELEMENT?
#590
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Prove with examples:-The set of all rational numbers except 0 are abelian group under multiplication.The set of all real numbers except 0 are closed under abelian group under multiplication.
#591
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Approach : 1.Select given number say 1, then find combination of rest of the elements. e.g select 1 , now remaining 4 elements, make subsets of 2 elements and add "1" in each subsets ie C(4,2) = 6. Suggest any another method please.
#592
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Can anyone help …. where I am wrong…??
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A binary operator ⊕ on a set of R - {-1} is defined as x ⊕ y = x + y + xy. Which of the following statement is true about(S, ⊕)?A)(S, ⊕) is group ... ) is monoid but not groupC)(S, ⊕) is semi-group but not monoidD)(S, ⊕) is abelian group
#594
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Are cosets, well ordered sets, total ordered sets in syllabus or GATE 2019?
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#596
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#597
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#598
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#599
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#600
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Consider the set H of all 3 3 matrices of the type:$\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$where a, b, c, d, e and f are real numbers ... but not a group(c) a semigroup but not a monoid(d) neither a group nor a semigroup