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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

#501
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Explain why $(A \times B) \times (C \times D)$ and $A \times (B \times C) \times D$ are not the same.
#502
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Explain why $A \times B \times C$ and $(A \times B) \times C$ are not the same.
#503
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Show that $A \times B \neq B \times A$, when $A$ and $B$ are nonempty. unless $A = B.$
#504
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How many different elements does $A^n$ have when $A$ has $m$ elements and $n$ is a positive integer?
#505
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How many different elements does $A \times B \times C$ have it $A$ has $m$ elemetns, $B$ has $n$ elements, and $C$ has $p$ elements?
#506
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How many different elements does $A \times B$ have if $A$ has $m$ elements and $B$ has $n$ elements?
#507
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Find $A^3$ if $A=\left \{ a \right \}$A= \left \{ 0,a \right \}$
#508
205
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1 votes
Find $A^2$ if$A = \left \{ 0,1,3 \right \}$A = \left \{ 1,2,a,b \right \}$
#509
281
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Let $A = \left \{ a,b,c \right \}$, $B = \left \{ x,y \right \},$ and $C= \left \{ 0,1 \right \}$. Find$A \times B \times C$C \times B \times A$C \times A \times B$B \times B \times B$
#510
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Let $A$ be a set. Show that $ \phi \times A = A \times \phi = \phi$
#511
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Suppose that $A \times B = \phi$, where $A$ and $B$ are sets. What can you conclude?
#512
240
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What is the Cartesian product $A \times B \times C$, where $A$ is the set of all airlines and $B$ and $C$ are both the set of all cities in the United States? Give an example of how this Cartesian product can be used.
#513
327
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What is the Cartesian product $A \times B$, where $A$ is the set of courses offered by the mathematics department at a university and $B$ is the ... professors at this university? Give an example of how this Cartesian product can be used.
#514
282
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1 answers
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Let $A = \left \{ a,b,c,d \right \}$ and $B= \left \{ y,z\right \}$ Find$A \times B.$B \times A.$
#515
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Show that if $A \subseteq C$ and $B \subseteq D$, then $A \times B \subseteq C \times D$
#516
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Prove that $P(A) \subseteq P(B)$ if and only if $A \subseteq B.$
#517
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Determine whether each of these sets is the power set of a set, where $a$ and $b$ are distinct elements.$\phi$ ...
#518
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How many elements does each of these sets have where $a$ and $b$ are distinct elements? $P (\left \{a,b, \left \{a,b \right \} \right \})$P\left \{ \phi, a, \left \{ a \right \},\left \{ \left \{ a \right \} \right \}\right \}$P(P(\phi ))$
#519
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Can you conclude that $A=B$ if $A$ and $B$ are two sets with the same power set?
#520
195
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Find the power set of each of these sets, where $a$ and $b$ are distinct elements{$a$}{$a,b$}{$\phi,$ {$\phi$}}