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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&0&1&2&1&1&0&2&0&0&0&0.8&2
\\\hline\textbf{2 Marks Count} & 0 &2&1&0&0&1&1&0&1&2&0&0.8&2
\\\hline\textbf{Total Marks} & 1&4&3&2&1&3&2&2&2&4&\bf{1}&\bf{2.4}&\bf{4}\\\hline
\end{array}}}$$

Recent questions in Set Theory & Algebra

2 votes

1 answer

101

Engineering Mathematics
why 4^10 is done. solution: Please explain the last portion why 4^ 10 is done.

why 4^10 is done.solution:Please explain the last portion why 4^ 10 is done.

543 views

Overflow04 asked Aug 22, 2022

1 votes

1 answer

102

maths igate test series
Which of the relations below can also be characterized as a function defined on the set I = { 1, 2, 3, 4, 5 } { (x, y) | x, y ∈ I, x < y } B{ (x, y) | x, y ∈ I, x = 1 } C{ (x, y) | x, y ∈ I, x! = y } None of these

Which of the relations below can also be characterized as a function defined on the setI = { 1, 2, 3, 4, 5 }{ (x, y) | x, y ∈ I, x < y }B{ (x, y) | x, y ∈ I, x = 1 }C...

499 views

jugnu1337 asked Aug 15, 2022

4 votes

1 answer

103

GO Classes Scholarship 2023 | Test | Question: 1
A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$. Which of the following options is/are false? Every Total relation is ... total and transitive, then $\mathrm{S}$ is an equivalence relation. The number of total relations on a set of $5$ elements is $1024.$

A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$.Which of the following optio...

964 views

GO Classes asked Aug 6, 2022

2 votes

3 answers

104

GO Classes Scholarship 2023 | Test | Question: 2
Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ ... such that $\forall j \neq i, x_{j}=y_{j}$ and $x_{i} \neq y_{i}$. What is the cardinality of relation $\mathrm{R}$?

Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ dif...

948 views

GO Classes asked Aug 6, 2022

4 votes

1 answer

105

GO Classes Scholarship 2023 | Test | Question: 3
Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathrm{S}$, let $\mathrm{S}^{\prime}$ be the set of those elements ...

Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathr...

518 views

GO Classes asked Aug 6, 2022

6 votes

2 answers

106

GO Classes Scholarship 2023 | Test | Question: 11
Let $\text{U}$ be a set and $\text{X, Y} \subseteq \text{U}$. Define operation twist by $ \operatorname{twist}\text{(X, Y)} =(\text{X} \cap \text{Y}) \cup(\overline{\text{X}} \cap \overline{\text{Y}}). $ Which of the following ... $\operatorname{twist}\text{(X, Y)}=\operatorname{twist}(\overline{\text{X}}, \overline{\text{Y}})$

Let $\text{U}$ be a set and $\text{X, Y} \subseteq \text{U}$. Define operation twist by$$\operatorname{twist}\text{(X, Y)} =(\text{X} \cap \text{Y}) \cup(\overline{\text{...

431 views

GO Classes asked Aug 6, 2022

0 votes

1 answer

107

Self doubt : Set Theory
At a family group meeting of 30 women, 17 are descended from George, 16 are descended from John, and 5 are not descended from George or John. How many of the 30 women are descended from both George and John?

At a family group meeting of 30 women, 17 are descended from George, 16 are descended from John, and 5 are not descended from George or John. How many of the 30 women are...

312 views

clendaya asked Aug 4, 2022

2 votes

2 answers

108

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 5
Consider the group $0,1,2,3,4,+{ }_{5}$. What will be the value of $2^{-3}$ and $3^{-2}$ for the given group? $1$ and $1$ $2$ and $3$ $4$ and $4$ $3$ and $2$

Consider the group $0,1,2,3,4,+{ }_{5}$. What will be the value of $2^{-3}$ and $3^{-2}$ for the given group?$1$ and $1$$2$ and $3$$4$ and $4$$3$ and $2$

432 views

GO Classes asked May 29, 2022

3 votes

1 answer

109

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 6
Let $f$ be a function from a set $X$ to a set $Y$. Consider the following statements. $P:$ For each $x \in X$, there exists $y \in Y$ such that $f(x)=y$. $Q$ : For each $y \in Y$, there exists $x \in X$ ... to-one and onto $Y$ " is $P$ or not $R$ $R$ or not $P$ $R$ or not $Q$ $P$ and not $R$

Let $f$ be a function from a set $X$ to a set $Y$. Consider the following statements.$P:$ For each $x \in X$, there exists $y \in Y$ such that $f(x)=y$.$Q$ : For each $y ...

363 views

GO Classes asked May 29, 2022

4 votes

1 answer

110

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 9
The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ with addition $\bmod n$ as the operation. How many subgroups of $Z_{9}$ are there?

The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ with addition $\bmod n$ as the operation.How many subgroups of $Z_{9}$ are there?

298 views

GO Classes asked May 29, 2022

4 votes

1 answer

111

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 10
Let $Z$ be the set of all integers. Let $n \in Z$ and $nZ = \{nk : k \in Z \}.$ We know that $Z$ is a group under addition operation. Which of the following is/are true? $nZ$ is a subgroup of $Z$ (under ... for some $n.$ $3Z$ is the smallest subgroup of $(Z,+)$ containing $3.$ $nZ$ is a cyclic subgroup of $Z.$

Let $Z$ be the set of all integers. Let $n \in Z$ and $nZ = \{nk : k \in Z \}.$ We know that $Z$ is a group under addition operation.Which of the following is/are true?$n...

531 views

GO Classes asked May 29, 2022

4 votes

1 answer

112

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 11
The set $Z_{\mathrm{n}}^{*}$ consists of the elements $\{1,2, \ldots, \mathrm{n}-1\}$ with multiplication $\bmod n$ as the operation. The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ ... then $\mathrm{G}$ is a cyclic group. The number of elements in $Z_{8}^{*}$ which have an inverse is $4.$

The set $Z_{\mathrm{n}}^{*}$ consists of the elements $\{1,2, \ldots, \mathrm{n}-1\}$ with multiplication $\bmod n$ as the operation.The group $Z_{n}$ consists of the ele...

288 views

GO Classes asked May 29, 2022

2 votes

1 answer

113

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 12
Consider the standard groups $Z_{\mathrm{n}}, \mathrm{R}^{*}, \mathrm{C}^{*}$ under their standard group operation. Here, $\mathrm{R}^{*}, \mathrm{C}^{*}$ are set of non-zero real numbers, set of non-zero complex numbers, ... $\sqrt{3} \in \mathrm{R}^{*}$ $-\mathrm{i} \in \mathrm{C}^{*}$

Consider the standard groups $Z_{\mathrm{n}}, \mathrm{R}^{*}, \mathrm{C}^{*}$ under their standard group operation. Here, $\mathrm{R}^{*}, \mathrm{C}^{*}$ are set of non-...

327 views

GO Classes asked May 29, 2022

5 votes

1 answer

114

GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 14
Let $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{g}: \mathrm{B} \rightarrow \mathrm{C}$ be maps. Which of the following is/are true? If $f$ and $g$ are both one-to-one functions, then $gof$ is one-to-one. ... $g \circ f$ is one-to-one and $f$ is onto, then $g$ is one-to-one.

Let $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{g}: \mathrm{B} \rightarrow \mathrm{C}$ be maps.Which of the following is/are true?If $f$ and $g$ are both...

309 views

GO Classes asked May 29, 2022

2 votes

1 answer

115

GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 6

Let $[N, \leq ]$ is a partial order relation defined on natural numbers, where “$\leq$” is the “less than equal to” relation defined on $N = \{ 0,1,2,3,\dots \}.$...

514 views

GO Classes asked May 12, 2022

3 votes

1 answer

116

GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 12

Let $R$ be a relation from a set $A$ to a set $B.$ The inverse relation from $B$ to $A,$ denoted by $R^{-1}$ , is the set of ordered pairs $\{(b,a) \mid (a,b) \in R\}$ .$...

421 views

GO Classes asked May 12, 2022

4 votes

1 answer

117

GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 13

For any integers $x,y,$ we say that $x$ divides $y$ iff there is some integer $z$ such that $y = x\ast z.$Let $[N, \leq]$ is a partial order relation defined on natural n...

528 views

GO Classes asked May 12, 2022

4 votes

2 answers

118

GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 14

Consider the following sentences :$[R, | ]$ is poset. Where $R$ is the set of all real numbers and $|$ is the divisibility relation i.e. for any $a,b$ in $R, a|b$ iff the...

674 views

GO Classes asked May 12, 2022

3 votes

1 answer

119

GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 15

Suppose $A$ is a finite set of five elements. Then the cardinality of the largest partial order relation possible on $A$ is _______

376 views

GO Classes asked May 12, 2022

4 votes

1 answer

120

GO Classes Test Series 2024 | Discrete Mathematics | Test 3 | Question: 2
Let $\text{G}$ be a cyclic group with generator ‘$a$’. Order of ‘$a$’ is $29.$ The number of subgroups $\text{G}$ has __________

Let $\text{G}$ be a cyclic group with generator ‘$a$’. Order of ‘$a$’ is $29.$ The number of subgroups $\text{G}$ has __________

516 views

GO Classes asked Apr 27, 2022

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