Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Q&A
Questions
Unanswered
Tags
Subjects
Users
Ask
Previous Years
Blogs
New Blog
Exams
Dark Mode
Recent questions and answers in Discrete Mathematics
21
votes
3
answers
1
GATE CSE 1992 | Question: 02,xvi
Which of the following is/are a tautology? $a \vee b \to b \wedge c$ $a \wedge b \to b \vee c$ $a \vee b \to \left(b \to c \right)$ $a \to b \to \left(b \to c \right)$
-RahulKumar-
answered
in
Mathematical Logic
7 hours
ago
by
-RahulKumar-
4.9k
views
gate1992
mathematical-logic
easy
propositional-logic
multiple-selects
26
votes
4
answers
2
GATE CSE 2001 | Question: 1.3
Consider two well-formed formulas in propositional logic $F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$ Which one of the following statements is correct? $F_1$ is satisfiable, $F_2$ is valid $F_1$ unsatisfiable, $F_2$ is satisfiable $F_1$ is unsatisfiable, $F_2$ is valid $F_1$ and $F_2$ are both satisfiable
-RahulKumar-
answered
in
Mathematical Logic
8 hours
ago
by
-RahulKumar-
7.1k
views
gatecse-2001
mathematical-logic
easy
propositional-logic
22
votes
6
answers
3
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 14
Consider the following popular puzzle. When asked for the ages of her three children, Mrs. Baker says that Alice is her youngest child if Bill is not her youngest child, and that Alice is not her youngest child if ... Bill is her youngest child. Carl is her youngest child. Information is not sufficient to find out the youngest child.
Soujit
answered
in
Mathematical Logic
1 day
ago
by
Soujit
1.2k
views
goclasses_wq5
goclasses2024_wq4
goclasses
mathematical-logic
propositional-logic
2-marks
0
votes
0
answers
4
discrete mathematics
The maximum number of edges possible in a graph G with 9 vertices which is 3 colourable is equal to A 24 B 27 C 36 D None of the above
someshawasthi
asked
in
Graph Theory
1 day
ago
by
someshawasthi
43
views
graph-theory
4
votes
4
answers
5
GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 5
How many rows appear in a truth table for this compound proposition? $(p \wedge r \wedge t) \leftrightarrow (q \wedge t)$
GauravRajpurohit
answered
in
Mathematical Logic
2 days
ago
by
GauravRajpurohit
361
views
goclasses_wq2
numerical-answers
goclasses
mathematical-logic
propositional-logic
1-mark
6
votes
4
answers
6
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 13
The number of combinations of truth values for $p, q$ and $r$ for which the statement $\neg p \leftrightarrow (q \wedge \neg (p \rightarrow r))$ is true ________
Sahil_Lather
answered
in
Mathematical Logic
2 days
ago
by
Sahil_Lather
395
views
goclasses
goclasses_wq3
goclasses2024_wq4
mathematical-logic
propositional-logic
numerical-answers
2-marks
3
votes
2
answers
7
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 10
Given the truth table of a Binary Operation \$ as follows: $ ... {array}$ Identify the matching Boolean Expression. $X \$ \neg Y$ $\neg X \$ Y$ $\neg X \$ \neg Y$ none of the options
sankalps
answered
in
Mathematical Logic
2 days
ago
by
sankalps
130
views
goclasses2024_wq4
goclasses
mathematical-logic
propositional-logic
2-marks
5
votes
4
answers
8
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 9
Let $P,S,R$ be three statements(propositions). Let $S$ be a sufficient condition for $P$, Let $R$ is a necessary condition for $P$ then which of the following is/are true? $S$ is a sufficient condition for $R$. $S$ is ... $S$ is neither sufficient, nor a necessary condition for $R.$ $S$ is a sufficient and necessary condition for $R$.
Sahil_Lather
answered
in
Mathematical Logic
2 days
ago
by
Sahil_Lather
480
views
goclasses_wq2
goclasses2024_wq4
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
3
votes
3
answers
9
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 3
Suppose that the statement $p \rightarrow \neg q$ is false. What is the number of all possible combinations of truth values of $r$ and $s$ for which $(\neg q \rightarrow r) \wedge (\neg p \vee s)$ is true?
Sahil_Lather
answered
in
Mathematical Logic
2 days
ago
by
Sahil_Lather
858
views
goclasses
goclasses_wq3
goclasses2024_wq4
mathematical-logic
propositional-logic
numerical-answers
1-mark
0
votes
2
answers
10
# propositional logic
Why “This statement is true” is proposition while “This statement is false” is liar paradox? Aren’t both statements supposed to be liar paradox ?
chokostar
answered
in
Mathematical Logic
3 days
ago
by
chokostar
206
views
mathematical-logic
propositional-logic
0
votes
1
answer
11
Kenneth Rosen Edition 7 Exercise 1.3 Question 13 (Page No. 35)
Use truth tables to verify the absorption laws. a) p ∨ (p ∧ q) ≡ p b) p ∧ (p ∨ q) ≡ p
chokostar
answered
in
Mathematical Logic
3 days
ago
by
chokostar
77
views
kenneth-rosen
discrete-mathematics
propositional-logic
1
vote
2
answers
12
#predicate-logic
Why "Birds can't fly" and "Every bird can't fly" are not same?
chokostar
answered
in
Mathematical Logic
3 days
ago
by
chokostar
109
views
discrete-mathematics
propositional-logic
0
votes
0
answers
13
kenneth rosen, counting, exercise: 6.5, question: 50
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?
Roshakaw
asked
in
Combinatory
5 days
ago
by
Roshakaw
24
views
discrete-mathematics
kenneth-rosen
0
votes
0
answers
14
Kenneth Rosen, exercise: 6.2, question: 8
Show that if f is a function from S to T , where S and T are finite sets with |S| > |T |, then there are elements s1 and s2 in S such that f (s1) = f (s2), or in other words, f is not one-to-one. How can I prove it by using “proof by contradiction”? Is it possible to prove the same by using “proof by contraposition”? If yes, how?
Roshakaw
asked
in
Combinatory
5 days
ago
by
Roshakaw
15
views
discrete-mathematics
kenneth-rosen
pigeonhole-principle
4
votes
2
answers
15
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 4
If $\mathbf{p}$ is true, $\mathbf{q}$ is true, and $\mathbf{r}$ is true, find the truth value of the statement. $ (p \wedge q) \leftrightarrow(q \vee \sim r) $ Choose the correct answer below. True because $(p \wedge q)$ ... and $(q \vee \sim r)$ is false. False because $(p \wedge q)$ is true and $(q \vee \sim r)$ is true.
GO Classes
asked
in
Mathematical Logic
6 days
ago
by
GO Classes
234
views
goclasses2024_wq4
goclasses
mathematical-logic
propositional-logic
1-mark
2
votes
2
answers
16
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 5
If $p$ is true and $q$ is false then the truth values of $(p \rightarrow q) \leftrightarrow(\sim q \rightarrow \sim p)$ and $(\sim p \vee \sim q) \wedge(\sim q \vee p)$ are respectively True, True True, False False, False False, True
GO Classes
asked
in
Mathematical Logic
6 days
ago
by
GO Classes
150
views
goclasses2024_wq4
goclasses
mathematical-logic
propositional-logic
1-mark
2
votes
2
answers
17
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 6
If $(p \wedge \sim q) \wedge(p \wedge r) \rightarrow \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are, respectively : $F, T, F$ $T, F, T$ $T, T, T$ $F, F, F$
GO Classes
asked
in
Mathematical Logic
6 days
ago
by
GO Classes
125
views
goclasses2024_wq4
goclasses
mathematical-logic
propositional-logic
1-mark
2
votes
3
answers
18
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 7
If $p, q, r$ are simple statement with truth values $T, F, T$ respectively then the truth value of $((\sim p \vee q) \wedge r) \rightarrow p$ is : True False True if $r$ is false True if $q$ is true
GO Classes
asked
in
Mathematical Logic
6 days
ago
by
GO Classes
141
views
goclasses2024_wq4
goclasses
mathematical-logic
propositional-logic
1-mark
6
votes
4
answers
19
GO Classes Weekly Quiz 4 | Propositional Logic | Question: 8
A very special island, "Smullyan's island", is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You encounter two people, $\text{A}$ and $\text{B. A}$ says " ... , respectively, if they address you in the above way described: Knight, Knight Knight, Knave Knave, Knight Knave, Knave
GO Classes
asked
in
Mathematical Logic
6 days
ago
by
GO Classes
231
views
goclasses2024_wq4
goclasses
mathematical-logic
propositional-logic
2-marks
0
votes
1
answer
20
#Eigen Vectors
Find the eigen values and eigen vector of the following matrix????
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Mar 21
by
Çșȇ ʛấẗẻ
52
views
eigen-value
linear-algebra
engineering-mathematics
matrix
0
votes
1
answer
21
self doubt
how to write if and only if symbolic form explain in detail????
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Mar 20
by
Çșȇ ʛấẗẻ
31
views
self-doubt
discrete-mathematics
matematical
mathematical-logic
0
votes
2
answers
22
Can any one solve this , 6B and 4G ,at least 2 girls should be together in circular arrangement
Shivank121
asked
in
Combinatory
Mar 19
by
Shivank121
52
views
discrete-mathematics
combinatory
0
votes
1
answer
23
explain universal quantifiers and existential quantifiers with example what is De morgan's law for quantifiers
gund pragati sunil
asked
in
Mathematical Logic
Mar 11
by
gund pragati sunil
59
views
mathematical-logic
0
votes
1
answer
24
explain with example, notations used and mathematical expressions to describe the following terms .i)membership ii) subset iii) equality of two sets iv) union
gund pragati sunil
asked
in
Mathematical Logic
Mar 11
by
gund pragati sunil
43
views
mathematical-logic
set-theory
2
votes
3
answers
25
NTRO exam 2023
the solution of the linear congruence 4x = 5(mod9)? 6 (mod 9) 8 (mod 9) 9(mod 9) 10 (mod 9)
jugnu1337
asked
in
Mathematical Logic
Mar 5
by
jugnu1337
204
views
discrete-mathematics
maths
1
vote
0
answers
26
Kenneth Rosen, exercise 6.1, Qs - 42 (d)
How many 4-element DNA sequences contain exactly three of the four bases A, T, C, and G? Solution given: There are four ways to choose which letter is to occur twice and three ways to decide which of the other letters to leave ... wrong. It would be of great help if you can show what combinations my approach is not including but the given solution includes.
Roshakaw
asked
in
Combinatory
Mar 3
by
Roshakaw
83
views
kenneth-rosen
discrete-mathematics
counting
combinatory
0
votes
2
answers
27
Discrete Maths by Kenneth Rosen, exercise 6.1, Qs - 12
How many bit strings are there of length six or less, not counting the empty string? Solution given:- We use the sum rule, adding the number of bit strings of each length up to 6. If we include the empty string, then we get 2^0 ... a binary string such as 000100 of length 3, and so on Please let me know if I am wrong somewhere in my approach.
Roshakaw
asked
in
Combinatory
Mar 2
by
Roshakaw
73
views
discrete-mathematics
kenneth-rosen
counting
0
votes
1
answer
28
set theory
If A = {1, 2, 3, . . . . . . 10} then the number of 4 element subsets of A containing ‘2’?
someshawasthi
asked
in
Set Theory & Algebra
Feb 27
by
someshawasthi
104
views
set-theory
0
votes
1
answer
29
#Combinatorics #Self doubt
How many 3 digits number are there which are divisible by 3 and repetition of digits NOT allowed.?
Hattbc
asked
in
Combinatory
Feb 17
by
Hattbc
191
views
counting
combinatory
0
votes
0
answers
30
#Graphs #Self_Doubt #Connectivity
What is a biconnected componenet?Does it always include V-V’ where V’ represent the set of articulation points of a graph G?
Gate Shark
asked
in
Graph Theory
Feb 17
by
Gate Shark
74
views
graph-theory
0
votes
0
answers
31
Kenneth Rosen Edition 7 Exercise 1.6 Question 11 (Page No. 79)
Show that the argument form with premises $p_1,p_2$,...,$p_n$ and conclusion q → r is valid if the argument form with premises $p_1,p_2,$...,$p_n$,q, and conclusion r is valid.
pavan singh
asked
in
Mathematical Logic
Feb 16
by
pavan singh
149
views
kenneth-rosen
discrete-mathematics
propositional-logic
4
votes
1
answer
32
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
admin
asked
in
Combinatory
Feb 15
by
admin
923
views
gatecse-2023
combinatory
recurrence-relation
1-mark
6
votes
3
answers
33
GATE CSE 2023 | Question: 16
Geetha has a conjecture about integers, which is of the form \[ \forall x(P(x) \Longrightarrow \exists y Q(x, y)), \] where $P$ is a statement about integers, and $Q$ is a statement about pairs of integers. Which of the following (one or more) option(s) would imply ... $\exists y \forall x(P(x) \Longrightarrow Q(x, y))$ $\exists x(P(x) \wedge \exists y Q(x, y))$
admin
asked
in
Mathematical Logic
Feb 15
by
admin
1.5k
views
gatecse-2023
mathematical-logic
first-order-logic
multiple-selects
1-mark
4
votes
0
answers
34
GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$
admin
asked
in
Combinatory
Feb 15
by
admin
956
views
gatecse-2023
combinatory
counting
2-marks
2
votes
1
answer
35
GATE CSE 2023 | Question: 39
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as \[ a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right), \] ... is NOT well-defined. $F$ is an onto (or surjective) function. $F$ is a one-to-one (or injective) function. $F$ is a bijective function.
admin
asked
in
Set Theory & Algebra
Feb 15
by
admin
891
views
gatecse-2023
set-theory&algebra
equivalence-class
multiple-selects
2-marks
2
votes
1
answer
36
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 $A$.
admin
asked
in
Set Theory & Algebra
Feb 15
by
admin
1.0k
views
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
4
votes
2
answers
37
GATE CSE 2023 | Question: 45
Let $G$ be a simple, finite, undirected graph with vertex set $\left\{v_{1}, \ldots, v_{n}\right\}$. Let $\Delta(G)$ denote the maximum degree of $G$ and let $\mathbb{N}=\{1,2, \ldots\}$ denote the set of all possible colors. Color the vertices ... $\Delta(G)$. The number of colors used is equal to the chromatic number of $G$.
admin
asked
in
Graph Theory
Feb 15
by
admin
2.1k
views
gatecse-2023
graph-theory
graph-coloring
multiple-selects
2-marks
0
votes
0
answers
38
Discrete Mathematics & Its Applications. Basic Structures - Sets, Functions, Sequences and Sums
N = {0,1,2,3 .} is the set of natural numbers. In Note, it is mentioned that some people do not consider 0 as a natural number. We know that set of Whole numbers is W = {0,1,2,3.. ... we consider 0 as an element in the set of Natural numbers, then what is the definition of Whole numbers in that scenario?
UdynGP
asked
in
Set Theory & Algebra
Feb 15
by
UdynGP
145
views
0
votes
1
answer
39
Kenneth Rosen Edition 7 Exercise 1.6 Question 10 (Page No. 79)
For each of these sets of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises. a) If I play hockey, then I am sore the next day. ... or hallucinating. I am not dreaming. If I am hallucinating, I see elephants running down the road.
pavan singh
asked
in
Mathematical Logic
Feb 13
by
pavan singh
184
views
kenneth-rosen
discrete-mathematics
propositional-logic
0
votes
2
answers
40
GATE CSE 2023 | Memory Based Question: 15
The Lucas sequence $L_n$ is defined by the recurrence relation: $L_n=L_{n-1}+L_{n-2}$, for $n \geq 3$ with $L_1=1$ and $L_2=3$. Which one of the options given is TRUE? $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{3}\right)^n$ ... $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{2}\right)^n$
closed
GO Classes
asked
in
Combinatory
Feb 6
by
GO Classes
460
views
memorybased-gatecse2023
goclasses
combinatory
recurrence-relation
To see more, click for all the
questions in this category
.
Subscribe to GATE CSE 2023 Test Series
Subscribe to GO Classes for GATE CSE 2023
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Central Pollution Control Board CPCB Various Post Recruitment 2023
MP Rajya Sahkari Apex Bank Various Post Recruitment 2023
NITIE MUMBAI throgh GATE
PGCIL recruitment 2023 – Apply Online For 138 Posts through GATE
Admission guidance for GATE CSE 2023
Subjects
All categories
General Aptitude
(2.6k)
Engineering Mathematics
(9.4k)
Discrete Mathematics
(6.5k)
Mathematical Logic
(2.2k)
Set Theory & Algebra
(1.7k)
Combinatory
(1.5k)
Graph Theory
(998)
Probability
(1.2k)
Linear Algebra
(909)
Calculus
(717)
Digital Logic
(3.3k)
Programming and DS
(5.9k)
Algorithms
(4.6k)
Theory of Computation
(6.7k)
Compiler Design
(2.3k)
Operating System
(5.0k)
Databases
(4.6k)
CO and Architecture
(3.8k)
Computer Networks
(4.7k)
Non GATE
(1.3k)
Others
(2.5k)
Admissions
(655)
Exam Queries
(847)
Tier 1 Placement Questions
(17)
Job Queries
(77)
Projects
(9)
Unknown Category
(866)
Recent questions and answers in Discrete Mathematics
Recent Blog Comments
Please see the updated link.
Unfortunately there won't be a hardcopy coming...
this book is not available on amazon now, i want...
Yes
Hi! @AnkitMazumder14 bhaiya,Is python...