Syllabus: Propositional and first order logic.

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\textbf{Year}&\textbf{2024-1}&\textbf{2024-2}&\textbf{2023}& \textbf{2022}& \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&0&1&1& 0 & 1&1&0&0.67&1
\\\hline\textbf{2 Marks Count}&0&0&0&0 & 0&0&0&0&0
\\\hline\textbf{Total Marks}& 0&1&1& 0 & 1&1&\bf{0}&\bf{0.67}&\bf{1}\\\hline
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Recent questions in Mathematical Logic

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101

Hasse Diagram

Çșȇ ʛấẗẻ

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Çșȇ ʛấẗẻ asked May 11, 2023

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0 answers

102

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?

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...

Chaitanya Kale

393 views

Chaitanya Kale asked May 10, 2023

0 votes

1 answer

103

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?????

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 correc...

pavan singh

740 views

pavan singh asked May 7, 2023

1 votes

1 answer

104

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

Prove or disprove (a) ∃x(P(x) ↔ Q(x)) → ¬∀xQ(x) ∨ ∃xP(x).

veer2000

242 views

veer2000 asked May 6, 2023

1 votes

1 answer

105

GO Classes 2024 | IIITH Mock Test 5 | Question: 11
Consider the following predicates: singular $(\mathrm{x}): \mathrm{x}$ is a singular matrix orthogonal $(\mathrm{x}): \mathrm{x}$ is an orthogonal matrix symmetric $(\mathrm{x}): \mathrm{x}$ is a symmetric matrix What is the ...

Consider the following predicates:singular $(\mathrm{x}): \mathrm{x}$ is a singular matrixorthogonal $(\mathrm{x}): \mathrm{x}$ is an orthogonal matrixsymmetric $(\mathrm...

GO Classes

178 views

GO Classes asked Apr 30, 2023

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0 answers

106

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]$

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

216 views

Hailemariam asked Apr 28, 2023

0 votes

0 answers

107

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

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

Hailemariam

148 views

Hailemariam asked Apr 28, 2023

0 votes

1 answer

108

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}).$

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}).$

Hailemariam

194 views

Hailemariam asked Apr 28, 2023

0 votes

1 answer

109

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

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

Hailemariam

200 views

Hailemariam asked Apr 28, 2023

0 votes

0 answers

110

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

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

Hailemariam

113 views

Hailemariam asked Apr 28, 2023

1 votes

4 answers

111

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

Ravi Ajagiya

431 views

Ravi Ajagiya asked Apr 25, 2023

0 votes

1 answer

112

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

[D6 , / ] is a poset ?

Ashutosh_17

312 views

Ashutosh_17 asked Apr 20, 2023

5 votes

3 answers

113

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 1
For a given predicate $\mathrm{P}(\mathrm{x}),$ you might believe that the statements $\forall \mathrm{xP}(\mathrm{x})$ or $\exists \mathrm{xP}(\mathrm{x})$ ... the domain, that $P(n)$ is true. Show for every element $n$ in the domain, that $P(n)$ is false.

For a given predicate $\mathrm{P}(\mathrm{x}),$ you might believe that the statements $\forall \mathrm{xP}(\mathrm{x})$ or $\exists \mathrm{xP}(\mathrm{x})$ are either tr...

GO Classes

459 views

GO Classes asked Apr 18, 2023

6 votes

3 answers

114

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 5
Consider the statement $\text{S} :$ "For all natural numbers $n,$ if $n$ is prime, then $n$ is antisocial." You do not need to know what antisocial means for this problem, just that it is a property ... $10$ is antisocial. $10$ is not antisocial. $7$ is antisocial. $7$ is not antisocial.

Consider the statement $\text{S} :$ "For all natural numbers $n,$ if $n$ is prime, then $n$ is antisocial."You do not need to know what antisocial means for this problem,...

GO Classes

461 views

GO Classes asked Apr 18, 2023

7 votes

2 answers

115

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 6
Suppose $P(x, y)$ is some binary predicate defined on a very small domain of discourse: just the integers $1,2,3$, and $4.$ For each of the $16$ pairs of these numbers, $P(x, y)$ is either true or false, according to the following ... $\exists x \forall y P(x, y)$. $\exists y \forall x P(x, y)$.

Suppose $P(x, y)$ is some binary predicate defined on a very small domain of discourse: just the integers $1,2,3$, and $4.$ For each of the $16$ pairs of these numbers, $...

GO Classes

306 views

GO Classes asked Apr 18, 2023

12 votes

2 answers

116

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 7
Let $P(x)$ and $Q(x)$ be predicates and let $D$ denote the domain of the predicate variable $x$. Consider the following universal conditional statement, $ \forall x \in D, P(x) \rightarrow Q(x) . $ Which of the following conditions ... is true for all $x \in D$. $P(x) \vee Q(x)$ is true for all $x \in D$.

Let $P(x)$ and $Q(x)$ be predicates and let $D$ denote the domain of the predicate variable $x$. Consider the following universal conditional statement,$$\forall x \in D,...

GO Classes

372 views

GO Classes asked Apr 18, 2023

6 votes

1 answer

117

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 8
Let $P(x), Q(x), R(x)$ and $S(x)$ denote the following predicates with domain $\mathbb{Z}$ ... $\forall x \in \mathbb{Z}, \quad S(x) \rightarrow(Q(x) \wedge S(x))$

Let $P(x), Q(x), R(x)$ and $S(x)$ denote the following predicates with domain $\mathbb{Z}$ :$$\begin{aligned}& P(x): x^2-x-12=0, \\& Q(x): x \text { is odd, } \\& R(x): x...

GO Classes

340 views

GO Classes asked Apr 18, 2023

9 votes

2 answers

118

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 15
Let's make a trip to a new world called "Never Never Land". Regular, ordinary first-order logic has two quantifiers: $\forall$ and $\exists$. Now, let's imagine we lived in a world in which these quantifiers ... $\mathrm{Nx}(\neg A(x) \wedge B(x))$

Let's make a trip to a new world called "Never Never Land".Regular, ordinary first-order logic has two quantifiers: $\forall$ and $\exists$.Now, let's imagine we lived in...

GO Classes

500 views

GO Classes asked Apr 18, 2023

1 votes

3 answers

119

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

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 )...

Jay Patel 009

530 views

Jay Patel 009 asked Apr 18, 2023

3 votes

2 answers

120

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

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 ...

ankitgupta.1729

537 views

ankitgupta.1729 asked Apr 15, 2023

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