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Hot questions in Discrete Mathematics
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161
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 57
A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ ... ; edges in its associated directed acyclic graph $G^{\prime}$ be $A, B$ respectively, then what is $A+B?$
GO Classes
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Graph Theory
Feb 5
by
GO Classes
497
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goclasses2024-mockgate-14
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40
votes
7
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162
GATE CSE 2005 | Question: 43
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto
gatecse
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gatecse
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0
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1
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163
GATE CSE 2024 | Set 1 | Question: 41
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$. Which of the following statements is/are always TRUE? $G$ contains a complete subgraph with ... $n/k$ $G$ contains at least $k(k-1) / 2$ edges $G$ contains a vertex of degree at least $k$
Arjun
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Graph Theory
Feb 16
by
Arjun
1.8k
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gatecse2024-set1
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graph-theory
45
votes
4
answers
164
GATE CSE 1996 | Question: 2.4
Which one of the following is false? The set of all bijective functions on a finite set forms a group under function composition The set $\{1, 2, \dots p-1\}$ forms a group under multiplication mod $p$, where $p$ is a prime number The set of all strings over a finite ... $\langle G, * \rangle$ if and only if for any pair of elements $a, b \in S, a * b^{-1} \in S$
Kathleen
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Set Theory & Algebra
Oct 9, 2014
by
Kathleen
9.6k
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gate1996
set-theory&algebra
normal
set-theory
group-theory
7
votes
2
answers
165
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 44
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the last character must be a digit, and any character that is a sign must be followed by a digit. There ... by $N_k=a N _{k-1}+b N _{k-2}$, for $k \geq 3$. What is $a+ b?$
GO Classes
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Combinatory
Jan 13
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GO Classes
533
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goclasses2024-mockgate-11
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2-marks
8
votes
1
answer
166
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 12
Let $A-B$ denote $\{x \in A: x \notin B\}$. If $(A-B) \cup B=A$, which of the following must be true? $B$ is empty $A \subseteq B$ $B \subseteq A$ $(B-A) \cup A=B$
GO Classes
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Set Theory & Algebra
Jan 13
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GO Classes
632
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goclasses2024-mockgate-11
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set-theory
1-mark
6
votes
2
answers
167
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 17
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the piles are also distinguishable?
GO Classes
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Combinatory
Jan 21
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GO Classes
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1-mark
8
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168
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 38
A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y R z$. Which of the following ... is transitive. If $R$ is a GO relation then $R$ is reflexive. If $R$ is an equivalence relation then $R$ is a GO relation.
GO Classes
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Set Theory & Algebra
Jan 13
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GO Classes
555
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goclasses2024-mockgate-11
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
4
votes
1
answer
169
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 46
Assume the following graph is a labeled graph i.e. every vertex has a unique label. In how many ways can we color the following labeled graph $\mathrm{G}$ with six colors $\{R, G, B, W, Y, M\}$ such that no two adjacent vertices are assigned the same color?
GO Classes
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Graph Theory
Jan 21
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GO Classes
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0
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170
Discrete mathematics Ch 1 : Propositional logic , Topic 2 : Logical operators or connectives
Which of the following is the negation of x is even iff x is divisible by 2 a) (x is even or x is not divisible by 2) and (x is not even or x is divisible by 2) b) (x is even and x is not divisible by 2) ... is divisible by 2) c) x is not even iff x is not divisible by 2 d) x is even if x is divisible by 2
lipishagupta
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Mathematical Logic
Mar 20
by
lipishagupta
66
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0
votes
2
answers
171
Kenneth Rosen Edition 7 Exercise 6.3 Question 26 (Page No. 414)
Thirteen people on a softball team show up for a game. How many ways are there to choose $10$ players to take the field? How many ways are there to assign the $10$ positions by selecting players from the $13$ people who show ... ways are there to choose $10$ players to take the field if at least one of these players must be a woman?
admin
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Combinatory
Apr 29, 2020
by
admin
4.4k
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kenneth-rosen
discrete-mathematics
counting
combinatory
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4
votes
1
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172
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 30
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the courses, and each course will have exactly one professor assigned to teach it. If any ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$
GO Classes
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Combinatory
Jan 28
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GO Classes
514
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goclasses2024-mockgate-13
goclasses
combinatory
counting
1-mark
28
votes
8
answers
173
GATE CSE 2008 | Question: 2
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
Kathleen
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Set Theory & Algebra
Sep 11, 2014
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Kathleen
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gatecse-2008
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4
votes
1
answer
174
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 62
As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is the set $ [x]_R=\{y \in A \mid x R y\} $ Let's now introduce some ... $\mathrm{I}(\mathrm{R})=n / 2$ and $\mathrm{W}(\mathrm{R})=n / 2$
GO Classes
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in
Set Theory & Algebra
Jan 28
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GO Classes
465
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goclasses2024-mockgate-13
goclasses
set-theory&algebra
set-theory
relations
equivalence-class
2-marks
0
votes
2
answers
175
Find no of sets A and B such that A n B = {3,5} and A U B = {2,3,5,7,8)
saisri
asked
in
Set Theory & Algebra
Mar 13
by
saisri
101
views
6
votes
1
answer
176
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 47
An involution is a function $f: A \rightarrow A$ where $f(f(x))=x$. A fixed point of any function $f: A \rightarrow A$ is an element $x \in A$ for which $f(x)$ $=x$. Which of the following statement(s) ... $f: \mathrm{A} \rightarrow \mathrm{A}$ is a bijective function.
GO Classes
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in
Set Theory & Algebra
Jan 21
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GO Classes
419
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goclasses2024-mockgate-12
goclasses
set-theory&algebra
functions
multiple-selects
2-marks
3
votes
1
answer
177
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are correct? The function $f$ must be one-to-one. The function $f$ must be onto. The function g must be one-to-one. The function $g$ must be onto.
GO Classes
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in
Set Theory & Algebra
Feb 5
by
GO Classes
466
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goclasses2024-mockgate-14
set-theory&algebra
functions
multiple-selects
2-marks
5
votes
2
answers
178
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 18
The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the objects are also indistinguishable?
GO Classes
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in
Combinatory
Jan 21
by
GO Classes
876
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goclasses2024-mockgate-12
goclasses
numerical-answers
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counting
1-mark
0
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1
answer
179
Does Either...Or means Exclusive Or or Inclusive Or?
Let's take a compound propositions Either it is below freezing or it is snowing. Now if $p$: it is below freezing $q$: it is snowing Will it be $p \vee q$ or $p \oplus q$? There are some instances where semantics are ... both cases can't be true, because if you are ill you can't appear for example and you must be in one state.
tbhaxor
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in
Mathematical Logic
Mar 12
by
tbhaxor
115
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propositional-logic
mathematical-logic
1
vote
1
answer
180
GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.6k
views
gatecse2024-set1
multiple-selects
set-theory&algebra
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