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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

#521
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What is the cardinality of each of these sets?$\phi${$\phi$}{$\phi$,{$\phi$}}{$\phi$, {$\phi$},{$\phi$, {$\phi$}}}
#522
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What is the cardinality of each of these sets?{$a$}{{$a$}}{$a$, {$a$}}{$a$,{$a$},{$a$, {$a$}}}
#523
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Find two sets $A$ and $B$ such that $A$ $\epsilon$ $B$ and $A \subset B.$
#524
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Suppose that $A, B,$ and $C$ are sets such that $A \subseteq B$ and $B \subseteq C.$ show that $A \subseteq C.$
#525
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Use a Venn diagram to illustrate the relationships $A \subset B$ and $B \subset C.$
#526
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Use a Venn diagram to illustrate the relationship $A \subseteq B$ and $B \subseteq C$.
#527
277
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1 votes
Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter $R$ in the set of all months of the year.
#528
282
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Use a Venn diagram to illustrate the subset of odd integers in the set of all positive integers not exceeding $10$.
#529
280
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Determine whether each of these statements is true or false.$x$ $\epsilon$ {$x$}{$x$} $\subset$ {$x$}{$x$} $\epsilon$ {$x$}{$x$} $\epsilon$ {{$x$}}$\phi$ $\subseteq$ {$x$}$\phi$ $\epsilon$ {$x$}
#530
476
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Determine whether each of these statements is true or false.$\phi$ $ \epsilon$ {$\phi$}$\phi$ $\epsilon$ {$\phi,$ { $\phi$}}{$\phi$} $ \epsilon$ {$ \phi$}{$\phi$ ... {$\phi$ , { $\phi$ }}{$\phi$} $\subset$ {{$\phi$ }, { $\phi$}}
#531
314
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For each of the following sets, determine whether 2 is an element of that set.$\{ x \in R \mid x \text{ is an integer greater than} \}$\{x \in R \mid x \text{ is the square of an integer ... $\{\{\{2\}\}\}$
#532
430
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Suppose that $A=$ { $2,4,6$ }, $B=$ { $2,6$ }, $C=$ { $4,6$ }, and $D=$ { $4,6,8$ }. Determine which of these sets are subsets of which other of these sets.
#533
357
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Determine whether each of these pairs of sets are equal.{ $1,3,3,3,5,5,5,5,5$ }, { $5,3,1$ }{{ $1$ }}, { $1$ , { $1$ }}$\phi$, { $\phi$ }
#534
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For each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first,or neither ... fruitsthe set of students studying discrete mathematics, the set of students studying data structures
#535
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For each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first, or neither is a subset ... who speak Chinesehe set of flying squirrels, the set of living creatures that can fly.
#536
222
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1 votes
Use set builder notation to give a description of each of these sets.{ $0,3,6,9,12$ }{ $-3,-2,-1,0,1,2,3$ }{ $ m,n,o,p$ }
#537
255
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List the numbers of these sets.{ $x$ | $x$ is a real number such that $x^2 =1$ }{ $x$ | $x$ is a positive integer less than 12 }{ $x$ | $x$ is the square of an integer and $x<100$ }{ $x$ | $x$ is an integer such that $x^2 =2$ }
#538
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R isiff $R ^{-1}$ isTotal?a function?a surjection?an injection?a bijection?Fill in the entries in the table.
#539
249
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Is the subset of a countably infinite set countable?
#540
580
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3 votes
Find ${\displaystyle \bigcup _{i=1}^{\infty }A_{i}} and \bigcup_{i=1}^{\infty} A_{i}$ if for every positive integer i,a) Ai = {i, i + 1, i + 2, . . .}.b) Ai = ... x with0 < x < i.d) Ai = (i,∞), that is, the set of real numbers x withx > i.