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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

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

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

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

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

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

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

130 views

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

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

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

206 views

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

77 views

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

109 views

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

24 views

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

15 views

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

234 views

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

150 views

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

125 views

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

141 views

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

231 views

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

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

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

52 views

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

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

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

204 views

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

83 views

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

73 views

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

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

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

74 views

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

149 views

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

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

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

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

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

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

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

184 views

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

460 views

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Recent questions and answers in Discrete Mathematics