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Recent questions in Discrete Mathematics
49
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6
answers
281
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 16
If $\text{F1, F2}$ and $\text{F3}$ are propositional formulae/expressions, over some set of propositional variables, such that $\mathrm{F} 1 \vee F 2 \rightarrow \mathrm{F} 3$ is a contradiction, then which of the following is/are ... is a tautology. $\text{F3}$ is a contradiction. $\text{F1} \mathrm{v} \text{F2}$ is a tautology.
GO Classes
asked
in
Mathematical Logic
Mar 26, 2023
by
GO Classes
1.6k
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
1
vote
1
answer
282
GO Classes 2023 | IIITH Mock Test 1 | Question: 1
Let $\text{R}$ be a relation from a set $\text{A}$ to a set $\text{B}.$ The inverse relation from $\text{B}$ to $\text{A},$ denoted by $\text{R}^{-1},$ is the set of ordered pairs $\{(b,a) \mid (a,b) \in R\}$ ... $\text{S1}$ Only $\text{S2}$ Both $\text{S1}$ and $\text{S2}$ None of the above
GO Classes
asked
in
Set Theory & Algebra
Mar 26, 2023
by
GO Classes
576
views
goclasses2023-iiith-mock-1
goclasses
set-theory&algebra
relations
1-mark
3
votes
2
answers
283
GO Classes 2023 | IIITH Mock Test 1 | Question: 2
Given a set of values $\text{R} = \{1,2,3,4,5,6,7\}.$ The number of relations on this set which are both partial-order and equivalence relation is? $128$ $1$ $0$ $2^{42}$
GO Classes
asked
in
Set Theory & Algebra
Mar 26, 2023
by
GO Classes
640
views
goclasses2023-iiith-mock-1
goclasses
set-theory&algebra
relations
partial-order
1-mark
6
votes
2
answers
284
GO Classes 2023 | IIITH Mock Test 1 | Question: 3
Let $\text{G}$ be a graph on $10$ vertices. We delete one vertex from $\text{G}.$ Since we have $10$ vertices, hence we get $10$ different subgraphs depending on which vertex we have deleted. Suppose that the number of edges in the vertex-deleted subgraphs of ... $\text{G}?$ $14$ $16$ $13$ $15$
GO Classes
asked
in
Graph Theory
Mar 26, 2023
by
GO Classes
785
views
goclasses2023-iiith-mock-1
goclasses
graph-theory
graph-connectivity
1-mark
3
votes
2
answers
285
GO Classes 2023 | IIITH Mock Test 1 | Question: 4
How many ways are there to arrange the $12$ letters of $\text{AAABBBBCCCCC}$ without having two $\text{Cs}$ together? $2652$ $1960$ $1826$ $2260$
GO Classes
asked
in
Combinatory
Mar 26, 2023
by
GO Classes
614
views
goclasses2023-iiith-mock-1
goclasses
combinatory
counting
1-mark
1
vote
1
answer
286
GO Classes 2023 | IIITH Mock Test 1 | Question: 5
$(\text{Q}, \ast)$ is an algebraic structure where $\text{Q}$ represents rational numbers and $\ast$ denotes multiplication. Which one of the following statements is true? $\text{Q}$ is an abelian group. $\text{Q}$ is a group but not abelian. $\text{Q}$ is a semigroup but not a monoid. $\text{Q}$ is monoid but not group.
GO Classes
asked
in
Set Theory & Algebra
Mar 26, 2023
by
GO Classes
533
views
goclasses2023-iiith-mock-1
goclasses
set-theory&algebra
group-theory
abelian-group
1-mark
2
votes
1
answer
287
GO Classes 2023 | IIITH Mock Test 1 | Question: 33
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ where $a_n = \binom {n+4}{n}$ for $n= 0,1,2,\ldots ?$ $\frac{1}{(1-x)^5}$ $\frac{5}{(1-x)}$ $\frac{1}{(1-x)^4}$ $\frac{x}{(1-x)^5}$
GO Classes
asked
in
Combinatory
Mar 26, 2023
by
GO Classes
535
views
goclasses2023-iiith-mock-1
goclasses
combinatory
generating-functions
1-mark
1
vote
0
answers
288
GO Classes 2023 | IIITH Mock Test 1 | Question: 41
Consider the following predicates. $\text{Rabbit}(x) = x$ is a rabbit. $\text{Cute}(x) = x$ is cute. Consider the following statement $\text{E},$ where the domain of every variable is set of all animals in a jungle $\text{J}.$ ... animal in $\text{J}$ who is not a rabbit but is cute. There is some rabbit who is cute in jungle $\text{J}.$
GO Classes
asked
in
Mathematical Logic
Mar 26, 2023
by
GO Classes
399
views
goclasses2023-iiith-mock-1
goclasses
mathematical-logic
first-order-logic
multiple-selects
1-mark
3
votes
1
answer
289
GO Classes 2023 | IIITH Mock Test 1 | Question: 42
Which of the following statements are correct? The complement of a simple disconnected graph must be connected. The complement of a simple connected graph must be disconnected. The complement of complete bipartite graph $\text{K}(4,6)$ has $10$ components. ... its complement. Then $\text{G}$ must have $4k$ or $4k + 1$ vertices for some integer $k.$
GO Classes
asked
in
Graph Theory
Mar 26, 2023
by
GO Classes
460
views
goclasses2023-iiith-mock-1
goclasses
graph-theory
graph-isomorphism
multiple-selects
1-mark
1
vote
0
answers
290
kenneth rosen, counting, exercise: 6.5, question: 50
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?
Pineapple
asked
in
Combinatory
Mar 23, 2023
by
Pineapple
266
views
discrete-mathematics
kenneth-rosen
0
votes
0
answers
291
Kenneth Rosen, exercise: 6.2, question: 8
Show that if f is a function from S to T , where S and T are finite sets with |S| > |T |, then there are elements s1 and s2 in S such that f (s1) = f (s2), or in other words, f is not one-to-one. How can I prove it by using “proof by contradiction”? Is it possible to prove the same by using “proof by contraposition”? If yes, how?
Pineapple
asked
in
Combinatory
Mar 23, 2023
by
Pineapple
264
views
discrete-mathematics
kenneth-rosen
pigeonhole-principle
0
votes
1
answer
292
#Eigen Vectors
Find the eigen values and eigen vector of the following matrix????
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Mar 21, 2023
by
Çșȇ ʛấẗẻ
1.2k
views
eigen-value
linear-algebra
engineering-mathematics
matrix
0
votes
1
answer
293
self doubt
how to write if and only if symbolic form explain in detail????
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Mar 20, 2023
by
Çșȇ ʛấẗẻ
382
views
self-doubt
discrete-mathematics
matematical
mathematical-logic
0
votes
2
answers
294
Can any one solve this , 6B and 4G ,at least 2 girls should be together in circular arrangement
Shivank121
asked
in
Combinatory
Mar 19, 2023
by
Shivank121
252
views
discrete-mathematics
combinatory
2
votes
2
answers
295
TIFR CSE 2023 | Part B | Question: 1
Consider the following two statements: $\text{(P)}$ The current population of Bhutan is greater than the current population of India. $\text{(Q)}$ The Moon is smaller than the Earth. Clearly, $\text{(P)}$ is false, while $\text{(Q)}$ is true. ... $\neg(\text{P} \Rightarrow \text{Q})$ $\text{P} \Leftrightarrow \text{Q}$ None of the above
admin
asked
in
Mathematical Logic
Mar 14, 2023
by
admin
652
views
tifr2023
mathematical-logic
propositional-logic
3
votes
1
answer
296
TIFR CSE 2023 | Part B | Question: 4
Amar, Balu, and Chhaya are three friends and they play the following game. Chhaya first chooses a number $k \in U$ where $U=\{1,2, \ldots, 127\}$. She either gives $k$ to both Amar and Balu, or else she gives $k$ to Amar and $k+1$ to Balu ... differed by $1.$ What is the minimal $n$ that allows Balu to distinguish between these two cases? $1$ $2$ $7$ $127$ $128$
admin
asked
in
Set Theory & Algebra
Mar 14, 2023
by
admin
388
views
tifr2023
set-theory&algebra
functions
5
votes
0
answers
297
TIFR CSE 2023 | Part B | Question: 10
A $d$-regular graph is one in which every vertex has degree $d$. Also, a minimum cut in a graph is a smallest set of edges which, upon removal, disconnects the graph, so that there are vertices in the resulting graph with no path between them. We are given two ... in $G_{2}$. Which of the following must be the size of this minimum cut? $0$ $1$ $2$ $3$ $4$
admin
asked
in
Graph Theory
Mar 14, 2023
by
admin
580
views
tifr2023
graph-theory
degree-of-graph
3
votes
0
answers
298
TIFR CSE 2023 | Part B | Question: 12
A graph $G=(V, E)$ is said to be $k$-colourable if the set $V$ of vertices can be coloured with $k$ colours such that no edge has both its endpoints of the same colour. It is known that the following language $\text{3COL}$ is $\text{NP}$-complete. \[ 3 \ ... $\text{(P1), (P3)}$and $\text{(P4)}$ Only problems $\text{(P1), (P2)}$and $\text{(P4)}$
admin
asked
in
Graph Theory
Mar 14, 2023
by
admin
351
views
tifr2023
graph-theory
graph-coloring
p-np-npc-nph
2
votes
1
answer
299
TIFR CSE 2023 | Part B | Question: 13
You have a regular tetrahedron and $4$ distinct colours. You wish to paint the faces of the tetrahedron such that each face gets a different colour. How many ways can you colour the tetrahedron? Recall that a regular tetrahedron is a three-dimensional ... considered the same if they are identical after possibly rotating the tetrahedron. $24$ $12$ $8$ $6$ $2$
admin
asked
in
Graph Theory
Mar 14, 2023
by
admin
468
views
tifr2023
graph-theory
graph-coloring
4
votes
1
answer
300
TIFR CSE 2023 | Part A | Question: 2
How many distinct rectangles can be formed using the vertices in the grid shown below? Squares are also counted as rectangles, and two rectangles are distinct if either their top-left vertices are different or their bottom-right vertices are different. ... $16$ $25$ $36$ $64$ $100$
admin
asked
in
Combinatory
Mar 14, 2023
by
admin
663
views
tifr2023
combinatory
counting
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