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Most viewed questions in Discrete Mathematics
42
votes
8
answers
121
GATE CSE 2004 | Question: 73
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
Kathleen
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Kathleen
12.8k
views
gatecse-2004
set-theory&algebra
partial-order
normal
43
votes
7
answers
122
GATE CSE 2015 Set 3 | Question: 41
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about $R$? Both reflexive and symmetric Reflexive but not symmetric Not reflexive but symmetric Neither reflexive nor symmetric
go_editor
asked
in
Set Theory & Algebra
Feb 15, 2015
by
go_editor
12.8k
views
gatecse-2015-set3
set-theory&algebra
relations
normal
3
votes
2
answers
123
If X and Y are two sets, then X⋂(Y⋃X) C equals
If X and Y are two sets, then X⋂(Y⋃X) C equals (a) X (b) Y (c) ϕ (d) None of these My attempt: X = {1,2,3} Y = {3,4,5} (Y⋃X) = {1,2,3,4,5} X⋂(Y⋃X) = {1,2,3} But the given answer is C
Prasanna
asked
in
Set Theory & Algebra
Nov 27, 2015
by
Prasanna
12.6k
views
set-theory&algebra
set-theory
37
votes
7
answers
124
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
Kathleen
asked
in
Graph Theory
Sep 18, 2014
by
Kathleen
12.6k
views
gatecse-2004
graph-theory
graph-coloring
easy
38
votes
9
answers
125
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
Kathleen
asked
in
Combinatory
Sep 14, 2014
by
Kathleen
12.6k
views
gatecse-2001
combinatory
normal
28
votes
6
answers
126
GATE CSE 2015 Set 2 | Question: 28
A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on $n$ vertices, $n$ is A multiple of 4 Even Odd Congruent to 0 $mod$ 4, or, 1 $mod$ 4.
go_editor
asked
in
Graph Theory
Feb 12, 2015
by
go_editor
12.6k
views
gatecse-2015-set2
graph-theory
graph-isomorphism
out-of-syllabus-now
27
votes
2
answers
127
GATE CSE 1990 | Question: 3-xi
A graph is planar if and only if, It does not contain a subgraph homeomorphic to $k_{5}$ and $k_{3, 3}$. It does not contain a subgraph isomorphic to $k_{5}$ and $k_{3, 3}$. It does not contain a subgraph isomorphic to $k_{5}$ or $k_{3, 3}$ It does not contain a subgraph homeomorphic to $k_{5}$ or $k_{3, 3}$.
makhdoom ghaya
asked
in
Graph Theory
Nov 23, 2016
by
makhdoom ghaya
12.5k
views
gate1990
normal
graph-theory
graph-planarity
multiple-selects
2
votes
1
answer
128
COMPLEMENT OF ELEMENT IN LATTICE
Parshu gate
asked
in
Set Theory & Algebra
Nov 6, 2017
by
Parshu gate
12.5k
views
lattice
set-theory&algebra
14
votes
5
answers
129
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
Shashank Mishra
asked
in
Set Theory & Algebra
Feb 4, 2019
by
Shashank Mishra
12.5k
views
48
votes
8
answers
130
GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
Kathleen
asked
in
Combinatory
Sep 21, 2014
by
Kathleen
12.5k
views
gatecse-2007
combinatory
60
votes
6
answers
131
GATE CSE 2014 Set 1 | Question: 50
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
12.4k
views
gatecse-2014-set1
set-theory&algebra
functions
combinatory
numerical-answers
30
votes
3
answers
132
GATE CSE 1998 | Question: 1.7
Let $R_1$ and $R_2$ be two equivalence relations on a set. Consider the following assertions: $R_1 \cup R_2$ is an equivalence relation $R_1 \cap R_2$ is an equivalence relation Which of the following is correct? Both assertions are true Assertions (i) is true ... (ii) is not true Assertions (ii) is true but assertions (i) is not true Neither (i) nor (ii) is true
Kathleen
asked
in
Set Theory & Algebra
Sep 25, 2014
by
Kathleen
12.4k
views
gate1998
set-theory&algebra
relations
normal
2
votes
1
answer
133
a graph with n vertices and n-1 edges that is not a tree is called
Anuanu
asked
in
Graph Theory
Jun 2, 2016
by
Anuanu
12.3k
views
graph-theory
tree
1
vote
1
answer
134
Kenneth Rosen Edition 6th Exercise 1.1 Question 9 (Page No. 17)
Let p and q be the propositions p : You drive over 65 miles per hour. q : You get a speeding ticket. Write these propositions using p and q and logical connectives (including negations). You do not drive over 65 miles per ... not drive over 65 miles per hour. Whenever you get a speeding ticket, you are driving over 65 miles per hour.
go_editor
asked
in
Mathematical Logic
Apr 14, 2016
by
go_editor
12.3k
views
kenneth-rosen
mathematical-logic
discrete-mathematics
28
votes
4
answers
135
GATE CSE 2018 | Question: 19
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
gatecse
asked
in
Set Theory & Algebra
Feb 14, 2018
by
gatecse
12.2k
views
gatecse-2018
group-theory
numerical-answers
set-theory&algebra
1-mark
32
votes
5
answers
136
GATE CSE 2018 | Question: 18
The chromatic number of the following graph is _____
gatecse
asked
in
Graph Theory
Feb 14, 2018
by
gatecse
12.1k
views
graph-theory
graph-coloring
numerical-answers
gatecse-2018
1-mark
57
votes
10
answers
137
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
khushtak
asked
in
Mathematical Logic
Feb 14, 2017
by
khushtak
12.1k
views
gatecse-2017-set2
mathematical-logic
propositional-logic
38
votes
7
answers
138
GATE CSE 1999 | Question: 2.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above
Kathleen
asked
in
Combinatory
Sep 23, 2014
by
Kathleen
12.1k
views
gate1999
combinatory
normal
47
votes
7
answers
139
GATE CSE 2000 | Question: 2.7
Let $a, b, c, d$ be propositions. Assume that the equivalence $a ⇔ ( b \vee \neg b)$ and $b ⇔c$ hold. Then the truth-value of the formula $(a ∧ b) → (a ∧ c) ∨ d$ is always True False Same as the truth-value of $b$ Same as the truth-value of $d$
Kathleen
asked
in
Mathematical Logic
Sep 14, 2014
by
Kathleen
12.0k
views
gatecse-2000
mathematical-logic
normal
propositional-logic
1
vote
2
answers
140
UGC NET CSE | December 2006 | Part 2 | Question: 3
The number of edges in a complete graph with $N$ vertices is equal to : $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$
go_editor
asked
in
Graph Theory
Mar 27, 2020
by
go_editor
12.0k
views
ugcnetcse-dec2006-paper2
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