Syllabus: Propositional and first order logic.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022}& \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}& 0 & 1&1&0&0&0&2&1&1&1&0&0.7&2
\\\hline\textbf{2 Marks Count}&0 & 0&0&1&1&1&1&0&0&1&0&0.5&1
\\\hline\textbf{Total Marks}& 0 & 1&1&2&2&2&4&1&1&3&\bf{0}&\bf{1.7}&\bf{4}\\\hline
\end{array}}}$$

Hot questions in Mathematical Logic

11 votes

2 answers

121

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

269 views

GO Classes asked Apr 18, 2023

33 votes

5 answers

122

GATE CSE 2004 | Question: 70
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above

The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not v...

Kathleen

7.6k views

Kathleen asked Sep 18, 2014

5 votes

5 answers

123

GO Classes CS 2025 | Weekly Quiz 1 | 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

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 :TrueFalseTrue if $r$ is ...

GO Classes

868 views

GO Classes asked Mar 22, 2023

3 votes

3 answers

124

GATE 2008 | Question 21
I have been trying to solve the question GATE CSE 2008 Question. Are the following two representations logically equivalent ? $\beta \rightarrow (\exists x, \alpha (x))$ $\exists x, \beta \rightarrow \alpha (x)$

I have been trying to solve the question GATE CSE 2008 Question.Are the following two representations logically equivalent ?$\beta \rightarrow (\exists x, \alpha (x))$$\e...

ParthPratim

1.0k views

ParthPratim asked Nov 3, 2022

1 votes

2 answers

125

Computer Science - UGC NET 2021 [ Question ID = 2351 ]
Which of the following are logically equivalent ? ¬p -> ( q -> r ) and q -> ( p v r ) ( p -> q ) -> r and p -> ( q -> r ) ( p -> q ) -> ( r -> s ) and ( p -> r) -> ( q -> s ) Choose the correct answer from the options given : i and ii only i and iii only i only ii and iii only

Which of the following are logically equivalent ?¬p - ( q - r ) and q - ( p v r )( p - q ) - r and p - ( q - r )( p - q ) - ( r - s ) and ( p - r) - ( q - s )Choose the ...

rajeshposts

670 views

rajeshposts asked Sep 14, 2023

9 votes

5 answers

126

GO Classes CS 2025 | Weekly Quiz 1 | 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 neither sufficient, nor a necessary condition for $R.$ $S$ is a sufficient and necessary condition for $R$.

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...

GO Classes

1.4k views

GO Classes asked May 2, 2022

0 votes

1 answer

127

Isomorphism

Çșȇ ʛấẗẻ

188 views

Çșȇ ʛấẗẻ asked Aug 28, 2023

0 votes

1 answer

128

#numbertheory
Prove that : In triangular series 1 = 1 1+2 = 3 1+2+3 = 6 1+2+3+4 = 10 ………….. Triangular number in 8n+1 always form perfect square .

Prove that :In triangular series1 = 11+2 = 31+2+3 = 61+2+3+4 = 10…………..Triangular number in 8n+1 always form perfect square .

NarutoUzumaki

167 views

NarutoUzumaki asked Oct 6, 2023

0 votes

1 answer

129

Set Theory

Çșȇ ʛấẗẻ

106 views

Çșȇ ʛấẗẻ asked Aug 28, 2023

0 votes

1 answer

130

Computer Science - UGC NET 2021 [ Question ID = 2352 ]
Which of these statements about the floor and ceiling functions are correct ? Statement 1 : ⌊2x⌋ = ⌊x⌋ + ⌊x + (1/2)⌋ for all real numbers x. Statement 2 : ⌈x + y⌉ = ⌈x⌉ + ⌈y⌉ for all real numbers x and y. Both ... I and Statement II are false. Statement I is true but Statement II is false. Statement I is false but Statement II is true.

Which of these statements about the floor and ceiling functions are correct ? Statement 1 : ⌊2x⌋ = ⌊x⌋ + ⌊x + (1/2)⌋ for all real numbers x.Statement 2 : ⌈x...

rajeshposts

298 views

rajeshposts asked Sep 16, 2023

12 votes

3 answers

131

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 11
Suppose that during the most recent fiscal year, the annual revenue of Acme Computer was $138$ billion dollars and its net profit was $8$ billion dollars, the annual revenue of Nadir Software was $87$ billion ... net profit. If Quixote Media had the smallest net profit, then Acme Computer had the largest annual revenue.

Suppose that during the most recent fiscal year, the annual revenue of Acme Computer was $138$ billion dollars and its net profit was $8$ billion dollars, the annual reve...

GO Classes

1.2k views

GO Classes asked May 2, 2022

0 votes

0 answers

132

Mathematical logic

suryansh rajput

278 views

suryansh rajput asked Oct 2, 2023

29 votes

10 answers

133

GATE CSE 1996 | Question: 2.3
Which of the following is NOT True? (Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication) $((x \rightarrow y) \wedge x) \rightarrow y$ ... $(x \rightarrow (x \vee y))$ $((x \vee y) \leftrightarrow (\neg x \rightarrow \neg y))$

Which of the following is NOT True?(Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication)...

Kathleen

8.4k views

Kathleen asked Oct 9, 2014

14 votes

4 answers

134

GO Classes CS 2025 | Weekly Quiz 1 | 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 $\text{B. A}$ ... respectively, if they address you in the above way described: Knight, Knight Knight, Knave Knave, Knight Knave, Knave

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, $\tex...

GO Classes

1.3k views

GO Classes asked Mar 22, 2023

3 votes

5 answers

135

GO Classes CS 2025 | Weekly Quiz 1 | 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

If $p$ is true and $q$ is false then the truth values of $(p \rightarrow q) \leftrightarrow(\sim q \rightarrow \sim p)$ and $(\sim p \vee \sim q) \wedge(\sim q \vee p)$ a...

GO Classes

735 views

GO Classes asked Mar 22, 2023

9 votes

2 answers

136

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 14
Let $\text{P}$ be a compound proposition over $4$ propositional variables $: a,b,c,d.$ We know that for a compound proposition over n propositional variables, we have $2^{n}$ rows in the truth table. Every row of the ... the sentence $(a \wedge b) \vee (b \wedge c)$ How many models are there for $\text{P}?$

Let $\text{P}$ be a compound proposition over $4$ propositional variables $: a,b,c,d.$We know that for a compound proposition over n propositional variables, we have $2^{...

GO Classes

525 views

GO Classes asked Apr 14, 2022

1 votes

1 answer

137

Digital Logic

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152 views

Çșȇ ʛấẗẻ asked Aug 28, 2023

43 votes

2 answers

138

GATE IT 2008 | Question: 22
Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, ¬y))]$ $[∀ x, ¬α → (∃y, ¬β → (∀u, ∃ v, ¬y))]$ $[∃ x, α \wedge (∀y, β \wedge (∃u, ∀ v, ¬y))]$

Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$$[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$$[∃ x, α → (∀y, β → ...

Ishrat Jahan

7.8k views

Ishrat Jahan asked Oct 27, 2014

16 votes

4 answers

139

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 10
In propositional logic if $\left ( P \rightarrow Q \right )\wedge \left ( R \rightarrow S \right )$ and $\left ( P \vee R \right )$ are two premises such that $\begin{array}{c} (P \to Q) \wedge (R \to S) \\ P \vee R \\ \hline Y \\ \hline \end{array}$ $Y$ is the premise : $P \vee R$ $P \vee S$ $Q \vee R$ $Q \vee S$

In propositional logic if $\left ( P \rightarrow Q \right )\wedge \left ( R \rightarrow S \right )$ and $\left ( P \vee R \right )$ are two premises such that$$\begin{arr...

GO Classes

854 views

GO Classes asked Mar 26, 2023

0 votes

1 answer

140

Theory of computation

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129 views

Çșȇ ʛấẗẻ asked Aug 28, 2023

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