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Recent questions and answers in Mathematical Logic

45 votes

8 answers

1

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

KG answered in Mathematical Logic May 25

by KG

8.5k views

1 vote

1 answer

2

GATE CSE 1988 | Question: 14ii
Consider the following well-formed formula: $\exists x \forall y [ \neg \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Show using resolution principle that the well-formed formula, given above, cannot be satisfied for any interpretation.

Ayushpal answered in Mathematical Logic May 24

427 views

89 votes

9 answers

3

GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.

uttsav1998 answered in Mathematical Logic May 23

15.6k views

0 votes

1 answer

4

self doubts
a’b’c+a’bc’+abc=?

Eswar01 answered in Mathematical Logic May 23

54 views

0 votes

1 answer

5

Find the value of [v]e wherev is a vector space and e is a list of polynomials

ankitgupta.1729 answered in Mathematical Logic May 18

by ankitgupta.1729

57 views

7 votes

2 answers

6

UGC NET CSE | December 2018 | Part 2 | Question: 1
In mathematical logic, which of the following are statements? There will be snow in January. What is the time now? Today is Sunday. You must study Discrete mathematics Choose the correct answer from the code given below: i and iii i and ii ii and iv iii and iv

itsayush007 answered in Mathematical Logic May 17

3.8k views

1 vote

1 answer

7

in proposition i have doubt in implication statement in p->q can i assume p->q is false when p is false ?

Samaroha answered in Mathematical Logic May 15

64 views

36 votes

7 answers

8

GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$

Soumen Mondal 1 answered in Mathematical Logic May 14

by Soumen Mondal 1

6.4k views

0 votes

0 answers

9

Let (1 + x)n = C0 + C1x + C2x2 + . . . + Cnxn, n being a positive integer. Then find the value of ( 1 + C0 C1 ) ( 1 + C1 C2 ) . . . ( 1 + Cn−1 Cn

JISAANNAGEORGE asked in Mathematical Logic May 11

by JISAANNAGEORGE

46 views

2 votes

1 answer

10

TIFR CSE 2023 | Part B | Question: 1
Consider the following two statements: $\text{(P)}$ The current population of Bhutan is greater than the current population of India. $\text{(Q)}$ The Moon is smaller than the Earth. Clearly, $\text{(P)}$ is false, while $\text{(Q)}$ is true. ... $\neg(\text{P} \Rightarrow \text{Q})$ $\text{P} \Leftrightarrow \text{Q}$ None of the above

csayan answered in Mathematical Logic May 11

by csayan

151 views

0 votes

0 answers

11

Generating Functions

Çșȇ ʛấẗẻ asked in Mathematical Logic May 11

by Çșȇ ʛấẗẻ

31 views

0 votes

0 answers

12

Çșȇ ʛấẗẻ asked in Mathematical Logic May 11

by Çșȇ ʛấẗẻ

38 views

0 votes

0 answers

13

Expectation of Random Variable
Consider a quiz where a person is given two questions and he must decide which question to answer first. Question 1 will be answered correctly with probability of 0.8 and the person will then receive as prize \ ... we sum P(X=0) + P(X=100) + P(X= 200) + P(X=300) = 2 Where I am getting wrong?

Chaitanya Kale asked in Mathematical Logic May 10

by Chaitanya Kale

54 views

18 votes

3 answers

14

GO Classes Weekly Quiz 5 | Propositional Logic | Question: 12
Two compound propositions are logically equivalent if they have the same truth table. For example, the following two compound propositions are logically equivalent: $\mathrm{p} \rightarrow \mathrm{q}$ ... propositional variables, how many compound propositions are there that are Not logically equivalent to each other?

ayush_27 answered in Mathematical Logic May 9

303 views

0 votes

1 answer

15

Proposition Logic doubt
Given: (p$ \vee$ q) is True. Find the truth value of statements, 1. p is false or q is true. (Can't determine) 2. If p is false then q is true. (True) is my answer correct?????

Durgesh_7979 answered in Mathematical Logic May 7

by Durgesh_7979

170 views

3 votes

1 answer

16

Kenneth Rosen Edition 7 Exercise 1.6 Question 28 (Page No. 80)
Use rules of inference to show that if $\forall x (P(x) \vee Q(x))$ and $\forall x ((\sim P(x) \wedge Q(x)) \rightarrow R(x))$ are true, then $\forall x (\sim R(x) \rightarrow P(x))$ is also true, where the domains of all quantifiers are the same.

thehitchh1ker answered in Mathematical Logic May 7

by thehitchh1ker

252 views

0 votes

1 answer

17

#discrete mathematics #1st order logic
Prove or disprove (a) ∃x(P(x) ↔ Q(x)) → ¬∀xQ(x) ∨ ∃xP(x).

d0t answered in Mathematical Logic May 6

by d0t

96 views

80 votes

5 answers

18

GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$

Akash 15 answered in Mathematical Logic May 1

12.4k views

0 votes

1 answer

19

Applied Mathematics-IB
Use the Squeeze Theorem to determine the value of $\lim_{x\rightarrow 0} x^{4}\sin (\frac{\pi}{x}).$x^{4}\sin (\frac{\pi}{x}).$

artim answered in Mathematical Logic Apr 30

by artim

36 views

50 votes

10 answers

20

GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$

KG answered in Mathematical Logic Apr 28

by KG

9.8k views

0 votes

0 answers

21

Applied Mathematics-IB
Determine all the number(s) c which satisfy the conclusion of Roles' Theorem for the given function and interval $f(x)=x^{2}-2x-8 $ on $ [-1,3]$

Hailemariam asked in Mathematical Logic Apr 28

52 views

0 votes

0 answers

22

Applied Mathematics-IB
sketch the graph of $h(x)=-(x+4)^{3}$ and identify all the relative extrema and absolute extrema of the function.

Hailemariam asked in Mathematical Logic Apr 28

15 views

0 votes

1 answer

23

Applied Mathematics-IB
Given that $7x\leq f\left ( x \right )\leq 3x^{2}+2$ for all determine the value of $\lim x\rightarrow 0 f(x)$

artim answered in Mathematical Logic Apr 28

by artim

37 views

0 votes

0 answers

24

Applied Mathematics-IB
1. Evaluate $x\rightarrow 5 lim (10)+\mid x-5\mid$

Hailemariam asked in Mathematical Logic Apr 28

49 views

10 votes

2 answers

25

GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 13
Consider the following list of $137$ statements: $\left(S_1\right): $ There is exactly $1$ false statement in this list. $\left(S_2\right): $ There are exactly $2$ ... true. It is possible that more than one statement in this list is true. Exactly one statement in this list is true.

zoy123 answered in Mathematical Logic Apr 27

by zoy123

203 views

51 votes

7 answers

26

GATE CSE 2003 | Question: 72
The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable

prajjwal_191 answered in Mathematical Logic Apr 25

by prajjwal_191

10.2k views

0 votes

1 answer

27

Discrete Maths Partial ordered set
[D6 , / ] is a poset ?

Ashutosh_17 asked in Mathematical Logic Apr 20

68 views

1 vote

3 answers

28

Discrete Mathematics | Predicate Logic
Which of the following conclusion can be drawn from the following premises $\left ( 1 \right )\sim P\vee Q\rightarrow R$ $\left ( 2 \right )S\vee \sim Q$ $\left ( 3 \right )\sim T$ $\left ( 4 \right )P\rightarrow T$ $\left ( 5 \right )\sim P\wedge R\rightarrow \sim S$ $C1: P$ $C2: \sim Q$ $C3: Q\wedge R$ C1 only C2 only C2 & C3 only C1 & C2 only

Jay Patel 009 asked in Mathematical Logic Apr 18

by Jay Patel 009

143 views

3 votes

2 answers

29

Discrete Mathematics | Propositional Logic | Test 2 | Question: 1
Let $\Phi$ be a well-formed formula having atleast one occurrence of atomic variable $x.$ Consider $\Psi$ be any formula. Now, $_x\Phi_{\Psi}$ is the formula obtained by replacing each occurrence of $x$ by $\Psi$ in $\Phi$ and ... Only (i) is correct Only (ii) is correct Both (i) and (ii) are correct None of the above

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

127 views

1 vote

1 answer

30

Discrete Mathematics | Propositional Logic | Test 2 | Question: 2
Consider the following argument: Either logic is difficult, or not many students like it. If mathematics is easy, then logic is not difficult. $\textit{Therefore,}$ if many students like logic, mathematics is not ... argument then $P \rightarrow Q$ is a tautology Validity of the given argument can't be determined

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

67 views

1 vote

1 answer

31

Discrete Mathematics | Propositional Logic | Test 2 | Question: 3
Suppose we have to construct a formula that expresses the truth function $\phi$ ... The formula that $\phi$ expresses is $\neg p \rightarrow ((p \rightarrow \neg p) \rightarrow (\neg p \rightarrow p))$

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

104 views

1 vote

1 answer

32

Discrete Mathematics | Propositional Logic | Test 2 | Question: 4
Consider a conditional statement $P \rightarrow Q.$ The proposition $Q \rightarrow P$ is called the $\textit{converse}$ of $P \rightarrow Q.$ The proposition $\neg Q \rightarrow \neg P$ ... If the converse is true, then the inverse is also logically true. (P and Q are distinct atomic sentences)

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

115 views

0 votes

1 answer

33

Discrete Mathematics | Propositional Logic | Test 2 | Question: 5
A compound proposition is $\textit{satisfiable}$ if there is an assignment of truth values to its variables that makes it true. When no such assignments exists, that is, when the compound proposition is false for all assignments of ... but not valid. Hence, it is a contingency where $P,Q$ and $R$ are distinct atomic propositions.

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

63 views

5 votes

2 answers

34

Discrete Mathematics | Propositional Logic | Test 2 | Question: 6
How many assignments of truth values to distinct $P_1,P_2,P_3,...,P_n$ with $n \geq 5$ ... $\textbf{Hint}:$ Try to construct the recurrence for the given problem and then solve it)

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

242 views

0 votes

1 answer

35

Discrete Mathematics | Propositional Logic | Test 2 | Question: 7
Suppose two premises are given as: $(1)$ Either Mary gives Peter his toy or Peter is going to cry. $(2)$ Mary does not give Peter his toy. Which one of the following statements is correct ? ... follows from the above two premises. Conclusion 'Peter is not going to cry' logically follows from the above two premises.

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

57 views

2 votes

1 answer

36

Discrete Mathematics | Propositional Logic | Test 2 | Question: 8
In the $\textit{theory of inference},$ we begin with a set of formulas which we call $\textit{premises/ hypotheses}$ and using some rules we obtain some other $\textit{given formula}$ ... a logical consequence of given premises Premise $(1)$ and $\neg C$ does not tautologically imply $S$

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

100 views

2 votes

2 answers

37

Discrete Mathematics | Propositional Logic | Test 2 | Question: 9
To decide an argument is $\textit{valid}$ with $n$ distinct premises as $P_1,P_2,...,P_n$ and conclusion $C$, we need to decide whether $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow C$ is tautology or not. Which of the ... $R,$ then we $\textit{can't}$ infer $R \rightarrow S$ from $P_1,P_2,...,P_n.$

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

156 views

1 vote

1 answer

38

Discrete Mathematics | Propositional Logic | Test 2 | Question: 10
Premises $P_1,P_2,...,P_n$ infer/derive a conclusion $Q$ if and only if the conditional $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow Q$ is a tautology. Consider the following statements: From $P$ ... $P$, $Q$ and $R$ are distinct atomic sentences ) Number of correct statements are ______

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

102 views

1 vote

2 answers

39

Discrete Mathematics | Propositional Logic | Test 2 | Question: 11
Consider the following argument: If either wages or prices are raised, there will be inflation. If there is inflation, then either Congress must regulate it or the people will suffer. If the people suffer, Congressmen will ... $P \rightarrow Q$ is a tautology. Validity of the given argument can't be determined.

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

120 views

4 votes

3 answers

40

Discrete Mathematics | Propositional Logic | Test 2 | Question: 12
Two sentences are said to be $\textit{contradictory}$ if one is negation of the other. A $\textit{contradiction}$ is a conjunction of two contradictory sentences i.e. it is a conjunction of the form $S \wedge \neg S.$ A set ... Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above

ankitgupta.1729 asked in Mathematical Logic Apr 16

by ankitgupta.1729

206 views

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