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Recent questions and answers in Discrete Mathematics
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Generating function doubt
Please give me clarification
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Combinatory
by
Sukannya
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discretemathematics
generatingfunctions
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2
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
answered
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Set Theory & Algebra
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Lakshman Patel RJIT
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gate2018
generatingfunctions
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+15
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4
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3
TIFR2010A12
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is. $2^{14}$ $31$ $\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) + 2\left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) \left ( \frac{10}{1} \right ) 2^{9}$
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7 hours
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Combinatory
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Lakshman Patel RJIT
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tifr2010
generatingfunctions
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4
Extended Binomial Coefficients
Find the value of extended Binomial Coefficient $\binom{1/2}{3}$
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Combinatory
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Mk Utkarsh
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permutationsandcombinations
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1
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5
Generating Function
How to apply this theorem to $\frac{x^{3}}{1x}$
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Set Theory & Algebra
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Lakshman Patel RJIT
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generatingfunctions
discretemathematics
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6
Sheldon Ross
From 10 married couples, we want to select group of 6 that is not allowed to contain a married couple. How many choices are there?
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Combinatory
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Yash Khanna
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161
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50
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sheldonross
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Self doubt generating function
Equation: x+y=10 and we are asked to find out the number of a nonnegative integral solution of this equation.
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Combinatory
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generatingfunctions
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Propositional logic
Both are valid right?
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Mathematical Logic
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Mk Utkarsh
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propositionallogic
+29
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8
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9
GATE20153_5
The number of 4 digit numbers having their digits in nondecreasing order (from left to right) constructed by using the digits belonging to the set {1, 2, 3} is ________.
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Combinatory
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Mk Utkarsh
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gate20153
permutationsandcombinations
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numericalanswers
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10
Sheldon Ross
Prove $\binom{m+n}{r}$ = $\binom{n}{0}\binom{m}{r}+\binom{n}{1}\binom{m}{r1}+... +\binom{n}{r}\binom{m}{0}$
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Combinatory
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Neelay Upadhyaya
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643
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42
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sheldonross
permutationsandcombinations
+11
votes
4
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11
GATE1993_8.2
The proposition $p \wedge (\sim p \vee q)$ is: a tautology logically equivalent to $p \wedge q$ logically equivalent to $p \vee q$ a contradiction none of the above
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Mathematical Logic
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gate1993
mathematicallogic
easy
propositionallogic
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1
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12
ISI2011A3b
The numbers 1, 2, . . . , 10 are arranged in a circle in some order. Show that it is always possible to find three adjacent numbers whose sum is at least 17, irrespective of the ordering.
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Set Theory & Algebra
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Mk Utkarsh
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descriptive
isi2011
pigeonhole
0
votes
0
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13
Self Doubt
Q) What would be the execution order of the below statement? A⟹B⟹C
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5 days
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Mathematical Logic
by
Lakshman Patel RJIT
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discretemathematics
+5
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3
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14
GATE201827
Let $N$ be the set of natural numbers. Consider the following sets, P: Set of Rational numbers (positive and negative) Q: Set of functions from {0,1} to $N$ R: Set of functions from $N$ to {0, 1} S: Set of finite subsets of $N$ Which of the above sets are countable? Q and S only P and S only P and R only P, Q and S only
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ago
in
Set Theory & Algebra
by
Neelay Upadhyaya
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643
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1.2k
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gate2018
settheory&algebra
#countableset
normal
+16
votes
10
answers
15
GATE2014353
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
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Mathematical Logic
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gate20143
mathematicallogic
easy
firstorderlogic
+13
votes
5
answers
16
GATE201411
Consider the statement "Not all that glitters is gold Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if x is gold. Which one of the following logical formulae represents the above statement? $\forall x: glitters (x)\ ... x)$ $\exists x: gold(x)\wedge \neg glitters(x)$ $\exists x: glitters(x)\wedge \neg gold(x)$
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Mathematical Logic
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Lakshman Patel RJIT
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gate20141
mathematicallogic
firstorderlogic
+21
votes
5
answers
17
GATE2013_27
What is the logical translation of the following statement? "None of my friends are perfect." (A) $∃x(F (x)∧ ¬P(x))$ (B) $∃ x(¬ F (x)∧ P(x))$ (C)$ ∃x(¬F (x)∧¬P(x))$ (D)$ ¬∃ x(F (x)∧ P(x))$
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5 days
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in
Mathematical Logic
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Lakshman Patel RJIT
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1.8k
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gate2013
mathematicallogic
easy
firstorderlogic
+13
votes
3
answers
18
GATE2012_13
What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” (A) $\exists x (real(x) \lor rational(x))$ (B) $\forall x (real(x) \to rational(x))$ (C) $\exists x (real(x) \wedge rational(x))$ (D) $\exists x (rational(x) \to real(x))$
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5 days
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in
Mathematical Logic
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Lakshman Patel RJIT
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845
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gate2012
mathematicallogic
easy
firstorderlogic
+14
votes
5
answers
19
GATE200926
Consider the following wellformed formulae: $\neg \forall x(P(x))$ $\neg \exists x(P(x))$ $\neg \exists x(\neg P(x))$ $\exists x(\neg P(x))$ Which of the above are equivalent? I and III I and IV II and III II and IV
answered
5 days
ago
in
Mathematical Logic
by
Lakshman Patel RJIT
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6.7k
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651
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gate2009
mathematicallogic
normal
firstorderlogic
+17
votes
4
answers
20
GATE200923
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ is precious $\forall x(P(x ... (G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$
answered
5 days
ago
in
Mathematical Logic
by
Lakshman Patel RJIT
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gate2009
mathematicallogic
easy
firstorderlogic
0
votes
0
answers
21
Sheldon Ross
Determine the number of vectors ($x_{1}...x_{n}$}, such that each x$_{i}$ is either 0 or 1 and $\sum_{i=1}^{n}x_{i}\geq k$
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5 days
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in
Combinatory
by
Tesla!
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14.4k
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50
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sheldonross
permutationsandcombinations
0
votes
1
answer
22
NIELIT ScientistB Dec 2017_24
Using bisection method, one root of X4X1 lies between 1 and 2. After second iteration the root may lie in interval : (A) (1.25, 1.5) (B) (1, 1.25) (C) (1, 1.5) (D) None of the options
answered
6 days
ago
in
Set Theory & Algebra
by
Manohar Kumar Sing 1
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13
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100
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0
votes
1
answer
23
Rosen Example 27
Q)Consider these statements, of which the first three are and fourth is a valid conclusion. "All hummingbirds are richly colored." "No large birds live on honey." "Birds that do not live on honey are dull in color" "Hummingbirds are small." Express using quantifiers??
answered
6 days
ago
in
Mathematical Logic
by
Mamta Satywali
Junior
(
631
points)

34
views
predicatelogic
kennethrosen
+1
vote
1
answer
24
Distributed Lattice
Is the following lattice distributed ?
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6 days
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in
Set Theory & Algebra
by
Mk Utkarsh
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118
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lattice
settheory&algebra
0
votes
0
answers
25
Rosen Example 25
Q) Use predicates and quantifiers to express the system specification "Every mail message larger than one megabyte will be compressed" and "If a user is active, at least one network link will be available."
[closed]
asked
6 days
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in
Mathematical Logic
by
Lakshman Patel RJIT
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38
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kennethrosen
predicatelogic
0
votes
1
answer
26
isro exam december 2017
The number of elements in the power set of {{1,2},{2,1,1},{2,1,1,2}} is:
answered
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ago
in
Set Theory & Algebra
by
saket nandan
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104
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isro2017
0
votes
0
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27
Graph theory
What is unorderd and ordered (if any) cycles in a given graph?
asked
Feb 16
in
Graph Theory
by
Sidd_
(
113
points)

32
views
+3
votes
7
answers
28
GATE201830
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements. No edge of $G$ is a cross edge with respect to $T_D$. (A cross edge in $G$ ... \mid =1$. Which of the statements above must necessarily be true? I only II only Both I and II Neither I nor II
answered
Feb 16
in
Graph Theory
by
suraj
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gate2018
graphtheory
normal
0
votes
1
answer
29
how to solve
answered
Feb 16
in
Set Theory & Algebra
by
Tesla!
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14.4k
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67
views
+4
votes
3
answers
30
GATE201828
Consider the firstorder logic sentence $$\varphi \equiv \exists \: s \: \exists \: t \: \exists \: u \: \forall \: v \: \forall \: w \forall \: x \: \forall \: y \: \psi(s, t, u, v, w, x, y)$$ where $\psi(s ... or equal to 3 There exists no model of $\varphi$ with universe size of greater than 7 Every model of $\varphi$ has a universe of size equal to 7
answered
Feb 15
in
Mathematical Logic
by
Sachin Mittal 1
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(
15.5k
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1.4k
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gate2018
mathematicallogic
normal
+3
votes
8
answers
31
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
answered
Feb 15
in
Combinatory
by
Kiran Kumar Pasupule
(
159
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1.7k
views
gate2018
permutationsandcombinations
heap
numericalanswers
+1
vote
4
answers
32
GATE201819
Let $G$ be a finite group on 84 elements. The size of a largest possible proper subgroup of $G$ is _____
answered
Feb 14
in
Set Theory & Algebra
by
RFITNES. TK
(
373
points)

1k
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gate2018
groups
numericalanswers
+4
votes
3
answers
33
GATE201818
The chromatic number of the following graph is _____
answered
Feb 14
in
Graph Theory
by
Syedarshadali
(
359
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938
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gate2018
graphtheory
chromaticnumber
numericalanswers
0
votes
0
answers
34
Closure of Relations
Let R be a relation on a set A. R may or may not have some property P, such as reflexivity, symmetry, or transitivity. If there is a relation S with property P containing R such that S is a subset of every relation with ... R, then S is called the closure Relations of R with respect to P. can someone explain this definition in simple words?
asked
Feb 14
in
Set Theory & Algebra
by
Mk Utkarsh
Boss
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7.1k
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30
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discretemathematics
kennethrosen
settheory&algebra
closureproperty
+1
vote
1
answer
35
Composition of functions
There exist 3 sets(A,B,C) and 2 functions f and g. g be a function from set A to set B f be a function from set B to set C then composition of both the functions is denoted by $f \circ g$ which exists. Then what ... condition for the following 2 functions for the existence of $g \circ f$ a) Injection b) Surjection c) Bijection d) None of these
answered
Feb 14
in
Set Theory & Algebra
by
shashanksingh
(
117
points)

65
views
discretemathematics
functions
+1
vote
0
answers
36
gate 2018
Consider the matrix P whose only Eigen vectors are the multiples of (1 4). Consider the following statements I. P does not have an inverse II. P has a repeated Eigen value. III. P cannot be diagonalized Which of the following Option is Correct?
asked
Feb 13
in
Mathematical Logic
by
Suryakant
(
51
points)

95
views
+1
vote
0
answers
37
Sequence
Conjecture a simple formula for an if the first few terms are 1,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4
asked
Feb 13
in
Set Theory & Algebra
by
Mk Utkarsh
Boss
(
7.1k
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35
views
sequenceseries
0
votes
1
answer
38
discrete maths
How many ordered pair of integers (a, b) are needed to guarantee that there are two ordered pairs (a1, b1) and (a2, b1) such that a1 mod 5 = a2 mod 5 and b1 mod 5 = b2 mod 5? should not answer be 25 here
answered
Feb 13
in
Graph Theory
by
Ayush Upadhyaya
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7.4k
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47
views
0
votes
1
answer
39
Self doubt
Let P(x) be the statement x spends more than five hours every weekday in class, where the domain for x consists of all students. Express each of these quantification in English. a) ∃xP(x) b) ∀xP(x) c) ∃x ¬P(x) d) ∀x ¬P(x) ... than 5 hours every weekday in class d) Every Student don't spend more than 5 hours every weekday in class Did all these are correct
answered
Feb 13
in
Mathematical Logic
by
Mk Utkarsh
Boss
(
7.1k
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25
views
0
votes
2
answers
40
Circular single linked list conceptual
answered
Feb 12
in
Mathematical Logic
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smsubham
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