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Hot questions in Discrete Mathematics
40
votes
9
answers
151
GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which ...
Kathleen
8.9k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
+
–
54
votes
6
answers
152
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
9.3k
views
Rucha Shelke
asked
Sep 18, 2014
Mathematical Logic
gatecse-2006
mathematical-logic
normal
first-order-logic
+
–
41
votes
5
answers
153
GATE CSE 2012 | Question: 37
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set? $ 2^{n}$ $2^{n} – 1$ $2^{n} – 2$ $2(2^{n} – 2)$
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set?$ 2^{n}$$2^{n} – 1$$2^{n} – 2$$2(2^{n} – 2)$
gatecse
9.4k
views
gatecse
asked
Sep 26, 2014
Set Theory & Algebra
gatecse-2012
set-theory&algebra
functions
normal
+
–
30
votes
5
answers
154
GATE CSE 1989 | Question: 14a
Symbolize the expression "Every mother loves her children" in predicate logic.
Symbolize the expression "Every mother loves her children" in predicate logic.
makhdoom ghaya
6.0k
views
makhdoom ghaya
asked
Dec 15, 2016
Mathematical Logic
gate1989
descriptive
first-order-logic
mathematical-logic
+
–
13
votes
1
answer
155
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 15
Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, a vertex of degree 5 , a vertex of degree 6 and ... of degree 7. Which of the following can be the degree of the last vertex? (Select all that are possible) 0 3 4 8
Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, ...
GO Classes
651
views
GO Classes
asked
Feb 5
Graph Theory
goclasses2024-mockgate-14
graph-theory
degree-of-graph
multiple-selects
1-mark
+
–
10
votes
1
answer
156
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 $A$.
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^{...
admin
5.6k
views
admin
asked
Feb 15, 2023
Set Theory & Algebra
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
+
–
27
votes
4
answers
157
GATE CSE 2010 | Question: 4
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ forms A Group A Ring An integral domain A field
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ formsA GroupA R...
gatecse
9.8k
views
gatecse
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2010
set-theory&algebra
normal
group-theory
+
–
34
votes
6
answers
158
GATE CSE 2004 | Question: 24
Consider the binary relation: $S= \left\{\left(x, y\right) \mid y=x+1 \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$ The reflexive transitive closure is $S$ ... $\left\{\left(x, y\right) \mid y \leq x \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$
Consider the binary relation:$S= \left\{\left(x, y\right) \mid y=x+1 \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$The reflexive transitive closure is $S$ is$\lef...
Kathleen
9.9k
views
Kathleen
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2004
set-theory&algebra
easy
relations
+
–
41
votes
3
answers
159
GATE CSE 1994 | Question: 1.10
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$? $g=g^{-1} \text{ for every } g \in G$ $g=g^2 \text{ for every }g \in G$ $(goh)^2 = g^2oh^2 \text{ for every } g, h \in G$ $G$ is of finite order
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$?$g=g^{-1} \text{ for every } g \in G$$g=g^2 \text{ for every }g \in G$$(goh)...
Kathleen
10.6k
views
Kathleen
asked
Oct 4, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
group-theory
normal
+
–
10
votes
1
answer
160
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 45
Below is a drawing(graph representation) of a binary relation $\text{R}$ over a set $\text{P}$ of elements $\{ \text{A, B, C, D, E, F}\}:$ Which of the following first-order logic statements about $\mathrm{R}$ ... $\forall x \in P . \exists y \in P . x R y$
Below is a drawing(graph representation) of a binary relation $\text{R}$ over a set $\text{P}$ of elements $\{ \text{A, B, C, D, E, F}\}:$Which of the following first-ord...
GO Classes
627
views
GO Classes
asked
Jan 21
Mathematical Logic
goclasses2024-mockgate-12
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
+
–
1
votes
2
answers
161
Does Either...Or means Exclusive Or or Inclusive Or?
Let's take a compound propositions Either it is below freezing or it is snowing. Now if $p$: it is below freezing $q$: it is snowing Will it be $p \vee q$ or $p \oplus q$? There are some instances where semantics are ... both cases can't be true, because if you are ill you can't appear for example and you must be in one state.
Let's take a compound propositionsEither it is below freezing or it is snowing.Now if$p$: it is below freezing $q$: it is snowingWill it be $p \vee q$ or $p \oplus q$? Th...
tbhaxor
167
views
tbhaxor
asked
Mar 12
Mathematical Logic
propositional-logic
mathematical-logic
+
–
43
votes
8
answers
162
GATE CSE 2007 | Question: 22
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ is connected. Which of the follo...
Kathleen
8.9k
views
Kathleen
asked
Sep 21, 2014
Mathematical Logic
gatecse-2007
mathematical-logic
easy
first-order-logic
+
–
2
votes
2
answers
163
Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\) \(\neg x \land y \Rightarrow \neg x \rightarrow y\) \(x \land \neg y \Rightarrow \neg x \rightarrow y\) \(\neg x \land y \Rightarrow y \rightarrow x\)
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\)\(\neg x \land y \Rightarrow \neg x \rightarrow y\)\(x \land \neg y \Rightarrow \ne...
GO Classes
245
views
GO Classes
asked
Feb 4
Mathematical Logic
gate2024-da-memory-based
goclasses
mathematical-logic
propositional-logic
+
–
43
votes
7
answers
164
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
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 ...
go_editor
12.9k
views
go_editor
asked
Feb 15, 2015
Set Theory & Algebra
gatecse-2015-set3
set-theory&algebra
relations
normal
+
–
0
votes
1
answer
165
ISI kolkata MTech CS 2019
Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths from $u$ to $v$ that do not contain the vertex $w$.
Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths fro...
suvasish114
34
views
suvasish114
asked
2 days
ago
Graph Theory
graph-theory
combinatory
isi2019-pcb-cs
+
–
0
votes
1
answer
166
self doubt
how to check the validity of an a argument using laws of logics
how to check the validity of an a argument using laws of logics
farhan777
32
views
farhan777
asked
4 days
ago
Mathematical Logic
self-doubt
discrete-mathematics
+
–
9
votes
1
answer
167
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 38
A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y R z$. Which of the following ... is transitive. If $R$ is a GO relation then $R$ is reflexive. If $R$ is an equivalence relation then $R$ is a GO relation.
A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y ...
GO Classes
566
views
GO Classes
asked
Jan 13
Set Theory & Algebra
goclasses2024-mockgate-11
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
+
–
0
votes
1
answer
168
Practice Material Question
If G is a connected graph with 6 vertices and maximum number of edges, then which of the following is true ? (a) Euler path exists, but Euler circuit does not exist in G. (b) Only Euler path exists in G. (c) Euler circuit does not exists in G (d) G is not traversable.
If G is a connected graph with 6 vertices and maximum number of edges, then which of the following is true ? (a) Euler path exists, but Euler circuit does not exist in G....
Akash Chakraborty
97
views
Akash Chakraborty
asked
Mar 30
Graph Theory
gate-preparation
graph-theory
+
–
0
votes
0
answers
169
Linear Algebra AX=B
Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly independent columns of B.
Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly in...
Soumya04
29
views
Soumya04
asked
2 days
ago
Mathematical Logic
linear-algebra
+
–
4
votes
1
answer
170
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are correct? The function $f$ must be one-to-one. The function $f$ must be onto. The function g must be one-to-one. The function $g$ must be onto.
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are...
GO Classes
525
views
GO Classes
asked
Feb 5
Set Theory & Algebra
goclasses2024-mockgate-14
set-theory&algebra
functions
multiple-selects
2-marks
+
–
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