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Highest voted questions in Discrete Mathematics
54
votes
6
answers
61
GATE CSE 1997 | Question: 6.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
The number of equivalence relations of the set $\{1,2,3,4\}$ is$15$$16$$24$$4$
Kathleen
21.2k
views
Kathleen
asked
Sep 29, 2014
Set Theory & Algebra
gate1997
set-theory&algebra
relations
normal
+
–
54
votes
6
answers
62
GATE CSE 2006 | Question: 26
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened. ...
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or ...
Rucha Shelke
9.1k
views
Rucha Shelke
asked
Sep 18, 2014
Mathematical Logic
gatecse-2006
mathematical-logic
normal
first-order-logic
+
–
54
votes
7
answers
63
GATE CSE 2009 | Question: 3
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices have the same degree. At least three vertices have the same degree. All vertices have the same degree.
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices ...
gatecse
11.3k
views
gatecse
asked
Sep 15, 2014
Graph Theory
gatecse-2009
graph-theory
normal
degree-of-graph
+
–
53
votes
5
answers
64
GATE CSE 2014 Set 3 | Question: 1
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.
Consider the following statements:P: Good mobile phones are not cheapQ: Cheap mobile phones are not goodL: P implies QM: Q implies PN: P is equivalent to QWhich one of th...
go_editor
10.5k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
gatecse-2014-set3
mathematical-logic
easy
propositional-logic
+
–
53
votes
5
answers
65
GATE CSE 2001 | Question: 2.2
Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ ... $S_2$? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Consider the following statements:$S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite.$S_2:$ There exists two irrational numbers $x$ a...
Kathleen
8.8k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
normal
set-theory
+
–
52
votes
6
answers
66
GATE CSE 2018 | Question: 27
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
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...
gatecse
21.7k
views
gatecse
asked
Feb 14, 2018
Set Theory & Algebra
gatecse-2018
set-theory&algebra
countable-uncountable-set
normal
2-marks
+
–
52
votes
8
answers
67
GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
What is the logical translation of the following statement?"None of my friends are perfect."$∃x(F (x)∧ ¬P(x))$$∃ x(¬ F (x)∧ P(x))$$ ∃x(¬F (x)∧¬P(x))$$ ¬�...
Arjun
14.0k
views
Arjun
asked
Sep 24, 2014
Mathematical Logic
gatecse-2013
mathematical-logic
easy
first-order-logic
+
–
52
votes
6
answers
68
GATE CSE 2001 | Question: 2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices?$\frac{n(n-1)} {2}$$2^n$$n!$$2^\f...
Kathleen
14.0k
views
Kathleen
asked
Sep 14, 2014
Graph Theory
gatecse-2001
graph-theory
normal
counting
+
–
52
votes
2
answers
69
GATE CSE 1991 | Question: 16,a
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's.$
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's....
Kathleen
6.4k
views
Kathleen
asked
Sep 12, 2014
Combinatory
gate1991
combinatory
normal
descriptive
catalan-number
+
–
51
votes
3
answers
70
GATE CSE 2015 Set 3 | Question: 23
Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T$. For any $T, R \in U \text{ let } T \backslash R$ be the set ... $X \backslash Y = \phi)$ $\forall X \in U, \forall Y \in U, (X \backslash Y = Y' \backslash X')$
Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T...
go_editor
11.9k
views
go_editor
asked
Feb 14, 2015
Set Theory & Algebra
gatecse-2015-set3
set-theory&algebra
set-theory
normal
+
–
51
votes
15
answers
71
GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
go_editor
19.2k
views
go_editor
asked
Feb 12, 2015
Set Theory & Algebra
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
+
–
51
votes
12
answers
72
GATE CSE 2014 Set 1 | Question: 53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ ... $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE?$(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge...
go_editor
13.4k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
gatecse-2014-set1
mathematical-logic
normal
propositional-logic
+
–
51
votes
5
answers
73
GATE CSE 2010 | Question: 1
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with $\xi(S) = \xi(T)$, then $| S| = 2| T |$ $| S | = | T | - 1$ $| S| = | T | $ $| S | = | T| + 1$
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with ...
gatecse
11.4k
views
gatecse
asked
Sep 21, 2014
Graph Theory
gatecse-2010
graph-theory
normal
degree-of-graph
+
–
51
votes
4
answers
74
GATE CSE 1991 | Question: 01,xv
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
Kathleen
11.4k
views
Kathleen
asked
Sep 12, 2014
Graph Theory
gate1991
graph-theory
graph-connectivity
normal
fill-in-the-blanks
+
–
50
votes
8
answers
75
GATE CSE 2016 Set 2 | Question: 26
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? ... and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions:$P:$ $R$ ...
Akash Kanase
14.5k
views
Akash Kanase
asked
Feb 12, 2016
Set Theory & Algebra
gatecse-2016-set2
set-theory&algebra
relations
normal
+
–
50
votes
9
answers
76
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Let $P(x)$ and $Q(x)$ be arbitrary predicates. Which of the following statements is always TRUE?$\left(\left(\forall x \left(P\left(x\right) \vee Q\left(x\right)\right)\r...
Ishrat Jahan
14.6k
views
Ishrat Jahan
asked
Nov 3, 2014
Mathematical Logic
gateit-2005
mathematical-logic
first-order-logic
normal
+
–
50
votes
4
answers
77
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
What is the first order predicate calculus statement equivalent to the following?"Every teacher is liked by some student"$∀(x)\left[\text{teacher}\left(x\right) → ∃...
gatecse
11.6k
views
gatecse
asked
Sep 21, 2014
Mathematical Logic
gatecse-2005
mathematical-logic
easy
first-order-logic
+
–
49
votes
11
answers
78
GATE CSE 2009 | Question: 2
What is the chromatic number of an $n$ vertex simple connected graph which does not contain any odd length cycle? Assume $n > 2$. $2$ $3$ $n-1$ $n$
What is the chromatic number of an $n$ vertex simple connected graph which does not contain any odd length cycle? Assume $n 2$.$2$$3$$n-1$ $n$
gatecse
13.0k
views
gatecse
asked
Sep 15, 2014
Graph Theory
gatecse-2009
graph-theory
graph-coloring
normal
+
–
49
votes
5
answers
79
GATE CSE 2001 | Question: 2.3
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S_1: f(E \cup F) = f(E) \cup f(F)$ $S_2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images.$S_1: f(E \cup F) = f(E) \cup f(F)$$S_2: f(E \cap F...
Kathleen
11.1k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
functions
normal
+
–
48
votes
10
answers
80
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \r...
Arjun
10.5k
views
Arjun
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
propositional-logic
+
–
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