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Recent questions in Discrete Mathematics
38
votes
9
answers
1921
GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
Let $G$ be an arbitrary group. Consider the following relations on $G$:$R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a ...
Arjun
17.4k
views
Arjun
asked
Feb 7, 2019
Set Theory & Algebra
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
+
–
33
votes
14
answers
1922
GATE CSE 2019 | Question: 12
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$
Let $G$ be an undirected complete graph on $n$ vertices, where $n 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to$n!$$(n-1)!$$1$$\frac{(n-1)!}{2}...
Arjun
21.4k
views
Arjun
asked
Feb 7, 2019
Graph Theory
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
1-mark
+
–
19
votes
18
answers
1923
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
The value of $3^{51} \text{ mod } 5$ is _____
Arjun
18.3k
views
Arjun
asked
Feb 7, 2019
Combinatory
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
+
–
68
votes
10
answers
1924
GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$
Consider the first order predicate formula $\varphi$:$\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w x) \wedge (\forall z \:...
Arjun
20.2k
views
Arjun
asked
Feb 7, 2019
Mathematical Logic
gatecse-2019
engineering-mathematics
discrete-mathematics
mathematical-logic
first-order-logic
2-marks
+
–
40
votes
6
answers
1925
GATE CSE 2019 | Question: 38
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
Let $G$ be any connected, weighted, undirected graph.$G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight.$G$ has a unique minimum spanning...
Arjun
20.6k
views
Arjun
asked
Feb 7, 2019
Graph Theory
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
2-marks
+
–
0
votes
2
answers
1926
#DiscreteMathematics #Rosen
“For every person x, if person x is a student in this class then x has studied Calculus.” S(x):Person x in the class C(x):x has studied Calculus. 1.$\vartheta _{x} (S(x) --> C(x))$ 2.$\vartheta _{x} (S(x) \Lambda C(x))$ Which one should hold? Why and why not?
“For every person x, if person x is a student in this class then x has studied Calculus.”S(x):Person x in the classC(x):x has studied Calculus.1.$\vartheta _{x} (S(x)...
Reshu $ingh
589
views
Reshu $ingh
asked
Feb 7, 2019
Mathematical Logic
discrete-mathematics
+
–
0
votes
1
answer
1927
Gate CS 2019
S1=Matrix is Invertible S2=Determinant of matrix is Non-zero What is the Answer..
S1=Matrix is InvertibleS2=Determinant of matrix is Non-zero What is the Answer..
rhtsya
606
views
rhtsya
asked
Feb 5, 2019
0
votes
1
answer
1928
GATE 2019
SOLVE: 2^32 mod 5
SOLVE: 2^32 mod 5
IITB2020
808
views
IITB2020
asked
Feb 5, 2019
0
votes
0
answers
1929
#math
Sankha Narayan Bose
333
views
Sankha Narayan Bose
asked
Feb 5, 2019
Set Theory & Algebra
gate19
+
–
14
votes
5
answers
1930
GATE 2019
Let U = {1, 2, ..., n} and A = {(x, X), x ∈ X and X ⊆ U}. Consider the following two statements for |A|. (i) |A| = n*$\small 2^{n-1}$ (ii) |A|= Sigma(k=1 to n) k.(nCk) Which of the following is correct? (a) (i) only (b) (ii) only (c) Both (i) and (ii) (d) None of the above
Let U = {1, 2, ..., n} and A = {(x, X), x ∈ X and X ⊆ U}. Consider the following twostatements for |A|.(i) |A| = n*$\small 2^{n-1}$(ii) |A|= Sigma(k=1 to n) k.(nCk) W...
Shashank Mishra
12.6k
views
Shashank Mishra
asked
Feb 4, 2019
0
votes
2
answers
1931
Gate 2019
What is the for the question where two statements were given as: S1: matrix A is invertible S2:|A|=0?
What is the for the question where two statements were given as:S1: matrix A is invertibleS2:|A|=0?
sai charan chakrala
952
views
sai charan chakrala
asked
Feb 4, 2019
0
votes
1
answer
1932
gate 2019
What is the answer for the predicate logic question,in which a formula was given and asked to find the sets satisying it?
What is the answer for the predicate logic question,in which a formula was given and asked to find the sets satisying it?
sai charan chakrala
347
views
sai charan chakrala
asked
Feb 4, 2019
0
votes
1
answer
1933
Gate cse 2109
What is the answer for question based on predicate logic ?
What is the answer for question based on predicate logic ?
Mounikap
780
views
Mounikap
asked
Feb 4, 2019
0
votes
0
answers
1934
gate 2019
Y is distributed uniformly in [1,6] 3x^2+6xY+3Y+6=0 P(Y) for 2 real roots ?
Y is distributed uniformly in [1,6]3x^2+6xY+3Y+6=0P(Y) for 2 real roots ?
jatin khachane 1
1.0k
views
jatin khachane 1
asked
Feb 4, 2019
0
votes
0
answers
1935
Fundamentals of Discrete Mathematics
Write the symbolic form? “If the utility cost goes up or the request for the additional funding is denied then a new computer will be purchased if and only if we can show that the current computing facilities are indeed not adequate.”
Write the symbolic form?“If the utility cost goes up or the request for the additional funding is denied then a new computer will be purchased if and only if we can sho...
tourist44
983
views
tourist44
asked
Feb 4, 2019
Mathematical Logic
discrete-mathematics
propositional-logic
+
–
0
votes
1
answer
1936
#GeneralMathematics
How to calculate modulus of an exponential number?
How to calculate modulus of an exponential number?
Reshu $ingh
748
views
Reshu $ingh
asked
Feb 3, 2019
Mathematical Logic
maths
+
–
0
votes
0
answers
1937
gate 2019
pream sagar
599
views
pream sagar
asked
Feb 3, 2019
0
votes
2
answers
1938
GATE2019
What is the total number of different Hamiltonian cycles for the complete graph of n vertices?
What is the total number of different Hamiltonian cycles for the complete graph of n vertices?
Atul Sharma 1
1.4k
views
Atul Sharma 1
asked
Feb 3, 2019
0
votes
0
answers
1939
Abelian group
A quick question Is every multiplication modulo function a Abelian group....Or is it the case that the function should have prime number as modulo
A quick question Is every multiplication modulo function a Abelian group....Or is it the case that the function should have prime number as modulo
Nandkishor3939
238
views
Nandkishor3939
asked
Feb 2, 2019
1
votes
1
answer
1940
Letters in boxes - combinations
Q .) The number of ways can 5 letter be put in 3 boxes A, B,C such that A has at least 2 letters. My approach: Number of ways to choose 2 letters out of 5 is 5C2. And for each such combination the remaining 3 letter have 3 choice. Therefore 5C2 * 3^3, but this is incorrect. Please point out the fault in my understanding and also the correct way to solve it
Q .) The number of ways can 5 letter be put in 3 boxes A, B,C such that A has at least 2 letters. My approach: Number of ways to choose 2 letters out of 5 is 5C2. And fo...
shaz
603
views
shaz
asked
Jan 31, 2019
Combinatory
combinatory
+
–
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