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Recent questions in Discrete Mathematics
5
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301
TIFR CSE 2023 | Part A | Question: 4
Let $\mathbb{R}$ be the set of all real numbers. Consider the relation $T$ defined as \[ T=\{(x, y) \in \mathbb{R} \times \mathbb{R} \text { such that } 4+x y>0\} \] $($Recall that ... but not symmetric an equivalence relation reflexive and symmetric but not transitive symmetric but not reflexive and not transitive symmetric and transitive but not reflexive
admin
asked
in
Set Theory & Algebra
Mar 14, 2023
by
admin
417
views
tifr2023
set-theory&algebra
relations
3
votes
1
answer
302
TIFR CSE 2023 | Part A | Question: 10
Let $Q$ be a set with $n$ elements. Consider a system with states of the form $(S, R)$ where $S \subseteq Q$ and $R \subseteq Q$, with the further restriction that $R \subseteq S$. Note that $(\emptyset, \emptyset)$ is also a valid state of the system (here $\emptyset$ ... have? $3^{n}$ $2^{n}$ $4^{n}$ $n^{3}$ $\left(\begin{array}{l}n \\ 3\end{array}\right)$
admin
asked
in
Set Theory & Algebra
Mar 14, 2023
by
admin
363
views
tifr2023
set-theory&algebra
set-theory
3
votes
1
answer
303
TIFR CSE 2023 | Part A | Question: 11
We are given a set $S=\left\{x_{1}, \ldots, x_{n}\right\}$ of distinct positive integers such that $\operatorname{gcd}\left(x_{i}, x_{j}\right)= 1$ for any $i, j \in\{1, \ldots, n\}$ where $i \neq j$. What is the total number of invertible $2 \times 2$ matrices whose entries are ... $n^{2}(n-1)^{2} / 4$ $n(n-1)(n-2)(n-3)$ $n(n-1)(n-2)(n-3) / 4$ !
admin
asked
in
Set Theory & Algebra
Mar 14, 2023
by
admin
302
views
tifr2023
set-theory&algebra
set-theory
3
votes
0
answers
304
TIFR CSE 2023 | Part A | Question: 12
Suppose is a piece on a chess board that attacks squares that are exactly two steps in the vertical direction, and squares that are adjacent horizontally (as marked with a "*" figure in the image below) What is the maximum number of these pieces that can ... other? (Note that each square is allowed to contain at most one piece.) $4$ $8$ $16$ $24$ $32$
admin
asked
in
Combinatory
Mar 14, 2023
by
admin
478
views
tifr2023
combinatory
counting
0
votes
1
answer
305
explain universal quantifiers and existential quantifiers with example what is De morgan's law for quantifiers
gund pragati sunil
asked
in
Mathematical Logic
Mar 10, 2023
by
gund pragati sunil
854
views
mathematical-logic
0
votes
1
answer
306
explain with example, notations used and mathematical expressions to describe the following terms .i)membership ii) subset iii) equality of two sets iv) union
gund pragati sunil
asked
in
Mathematical Logic
Mar 10, 2023
by
gund pragati sunil
1.1k
views
mathematical-logic
set-theory
3
votes
3
answers
307
NTRO exam 2023
the solution of the linear congruence 4x = 5(mod9)? 6 (mod 9) 8 (mod 9) 9(mod 9) 10 (mod 9)
jugnu1337
asked
in
Mathematical Logic
Mar 5, 2023
by
jugnu1337
1.9k
views
discrete-mathematics
maths
1
vote
0
answers
308
Kenneth Rosen, exercise 6.1, Qs - 42 (d)
How many 4-element DNA sequences contain exactly three of the four bases A, T, C, and G? Solution given: There are four ways to choose which letter is to occur twice and three ways to decide which of the other letters to leave ... wrong. It would be of great help if you can show what combinations my approach is not including but the given solution includes.
Pineapple
asked
in
Combinatory
Mar 3, 2023
by
Pineapple
1.1k
views
kenneth-rosen
discrete-mathematics
counting
combinatory
0
votes
1
answer
309
set theory
If A = {1, 2, 3, . . . . . . 10} then the number of 4 element subsets of A containing ‘2’?
someshawasthi
asked
in
Set Theory & Algebra
Feb 27, 2023
by
someshawasthi
372
views
set-theory
1
vote
1
answer
310
#Combinatorics #Self doubt
How many 3 digits number are there which are divisible by 3 and repetition of digits NOT allowed.?
Hattbc
asked
in
Combinatory
Feb 17, 2023
by
Hattbc
510
views
counting
combinatory
0
votes
0
answers
311
#Graphs #Self_Doubt #Connectivity
What is a biconnected componenet?Does it always include V-V’ where V’ represent the set of articulation points of a graph G?
Psy Duck
asked
in
Graph Theory
Feb 17, 2023
by
Psy Duck
385
views
graph-theory
0
votes
0
answers
312
Kenneth Rosen Edition 7 Exercise 1.6 Question 11 (Page No. 79)
Show that the argument form with premises $p_1,p_2$,...,$p_n$ and conclusion q → r is valid if the argument form with premises $p_1,p_2,$...,$p_n$,q, and conclusion r is valid.
pavan singh
asked
in
Mathematical Logic
Feb 16, 2023
by
pavan singh
858
views
kenneth-rosen
discrete-mathematics
propositional-logic
7
votes
4
answers
313
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
admin
asked
in
Combinatory
Feb 15, 2023
by
admin
7.8k
views
gatecse-2023
combinatory
recurrence-relation
1-mark
23
votes
5
answers
314
GATE CSE 2023 | Question: 16
Geetha has a conjecture about integers, which is of the form \[ \forall x(P(x) \Longrightarrow \exists y Q(x, y)), \] where $P$ is a statement about integers, and $Q$ is a statement about pairs of integers. Which of the following (one or more) option(s) would imply ... $\exists y \forall x(P(x) \Longrightarrow Q(x, y))$ $\exists x(P(x) \wedge \exists y Q(x, y))$
admin
asked
in
Mathematical Logic
Feb 15, 2023
by
admin
11.0k
views
gatecse-2023
mathematical-logic
first-order-logic
multiple-selects
1-mark
14
votes
3
answers
315
GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$
admin
asked
in
Combinatory
Feb 15, 2023
by
admin
6.3k
views
gatecse-2023
combinatory
counting
2-marks
11
votes
2
answers
316
GATE CSE 2023 | Question: 39
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as \[ a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right), \] ... is NOT well-defined. $F$ is an onto (or surjective) function. $F$ is a one-to-one (or injective) function. $F$ is a bijective function.
admin
asked
in
Set Theory & Algebra
Feb 15, 2023
by
admin
5.7k
views
gatecse-2023
set-theory&algebra
equivalence-class
multiple-selects
2-marks
10
votes
1
answer
317
GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.
admin
asked
in
Set Theory & Algebra
Feb 15, 2023
by
admin
5.5k
views
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
7
votes
3
answers
318
GATE CSE 2023 | Question: 45
Let $G$ be a simple, finite, undirected graph with vertex set $\left\{v_{1}, \ldots, v_{n}\right\}$. Let $\Delta(G)$ denote the maximum degree of $G$ and let $\mathbb{N}=\{1,2, \ldots\}$ denote the set of all possible colors. Color the vertices ... $\Delta(G)$. The number of colors used is equal to the chromatic number of $G$.
admin
asked
in
Graph Theory
Feb 15, 2023
by
admin
8.1k
views
gatecse-2023
graph-theory
graph-coloring
multiple-selects
2-marks
0
votes
0
answers
319
Discrete Mathematics & Its Applications. Basic Structures - Sets, Functions, Sequences and Sums
N = {0,1,2,3 .} is the set of natural numbers. In Note, it is mentioned that some people do not consider 0 as a natural number. We know that set of Whole numbers is W = {0,1,2,3.. ... we consider 0 as an element in the set of Natural numbers, then what is the definition of Whole numbers in that scenario?
UdynGP
asked
in
Set Theory & Algebra
Feb 15, 2023
by
UdynGP
436
views
0
votes
1
answer
320
Kenneth Rosen Edition 7 Exercise 1.6 Question 10 (Page No. 79)
For each of these sets of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises. a) If I play hockey, then I am sore the next day. ... or hallucinating. I am not dreaming. If I am hallucinating, I see elephants running down the road.
pavan singh
asked
in
Mathematical Logic
Feb 13, 2023
by
pavan singh
3.3k
views
kenneth-rosen
discrete-mathematics
propositional-logic
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