Recent questions tagged mathematical-logic / GATE Overflow for GATE CSE

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GO 2023 Topic Wise Free Test 2 | First Order Logic | Question: 12
Let $\varphi$ be a propositional formula on a set of variables $A$ and $\psi$ be a propositional formula on a set of variables $B$ , such that $\varphi$ $\Rightarrow$ $\psi$ . A $\textit{Craig interpolant}$ of $\varphi$ and $\psi$ is ... interpolant for $\varphi$ and $\psi?$ $\varphi$ itself $q \vee s$ $q \vee r$ $\neg q \wedge s$

Let $\varphi$ be a propositional formula on a set of variables $A$ and $\psi$ be a propositional formula on a set of variables $B$ , such that $\varphi$ $\Rightarrow$...

GO Classes

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GO Classes asked Dec 13, 2022

4 votes

2 answers

212

GO 2023 Topic Wise Free Test 2 | First Order Logic | Question: 13
Which of the following formulas does not express that there is exactly one element of $\text{D}$ that has property $\text{P}(x)?$ $\exists x \in \text{D} \forall y \in \text{D}[\text{P}(y) \leftrightarrow y=x]$ ... $\exists x \in \text{D} \forall y \in \text{D}[\text{P}(y) \rightarrow y=x]$

Which of the following formulas does not express that there is exactly one element of $\text{D}$ that has property $\text{P}(x)?$$\exists x \in \text{D} \forall y \in \te...

GO Classes

182 views

GO Classes asked Dec 13, 2022

1 votes

1 answer

213

First Order Logic: Gate@Zeal Test series

Shoto

775 views

Shoto asked Dec 12, 2022

0 votes

2 answers

214

# 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 ?

Why“This statement is true” is proposition while “This statement is false” is liar paradox?Aren’t both statements supposed to be liar paradox ?

Aditi Thakur

536 views

Aditi Thakur asked Dec 7, 2022

2 votes

0 answers

215

GO 2023 Topic Wise Free Test 1 | Question: 1
What is logically equivalent to "If Kareena and Parineeti go to the shopping mall then it is raining": If Kareena and Parineeti do not go to the shopping mall then it is not raining. If Kareena and Parineeti do not go to the ... Parineeti go to the shopping mall. If it is not raining then Kareena and Parineeti do not go to the shopping mall.

What is logically equivalent to "If Kareena and Parineeti go to the shopping mall then it is raining":If Kareena and Parineeti do not go to the shopping mall then it is n...

GO Classes

148 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

216

GO 2023 Topic Wise Free Test 1 | Question: 2
Which of the following expressions is false? $p \rightarrow q \equiv q \rightarrow p$ $\neg(p \vee q) \equiv \neg p \wedge \neg q$ $p \rightarrow q \equiv \neg q \rightarrow \neg p$ none of the above

Which of the following expressions is false?$p \rightarrow q \equiv q \rightarrow p$$\neg(p \vee q) \equiv \neg p \wedge \neg q$$p \rightarrow q \equiv \neg q \rightarrow...

GO Classes

144 views

GO Classes asked Dec 5, 2022

2 votes

0 answers

217

GO 2023 Topic Wise Free Test 1 | Question: 3
Which of the following expressions is always true? $\neg p \vee p$ $\neg p \wedge p$ $\neg p \wedge \neg p$ none of the above

Which of the following expressions is always true?$\neg p \vee p$$\neg p \wedge p$$\neg p \wedge \neg p$none of the above

GO Classes

112 views

GO Classes asked Dec 5, 2022

2 votes

0 answers

218

GO 2023 Topic Wise Free Test 1 | Question: 4
Select the proposition that is a tautology. $(p \wedge q) \rightarrow \neg p$ $(p \vee q) \rightarrow p$ $(p \wedge q) \leftrightarrow p$ $(p \wedge q) \rightarrow p$

Select the proposition that is a tautology.$(p \wedge q) \rightarrow \neg p$$(p \vee q) \rightarrow p$$(p \wedge q) \leftrightarrow p$$(p \wedge q) \rightarrow p$

GO Classes

134 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

219

GO 2023 Topic Wise Free Test 1 | Question: 5
Select the proposition that is a contradiction. $\neg(p \vee q) \wedge p$ $(p \vee q) \wedge p$ $(\neg p \wedge q) \leftrightarrow p$ $(\neg p \wedge q) \rightarrow p$

Select the proposition that is a contradiction.$\neg(p \vee q) \wedge p$$(p \vee q) \wedge p$$(\neg p \wedge q) \leftrightarrow p$$(\neg p \wedge q) \rightarrow p$

GO Classes

170 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

220

GO 2023 Topic Wise Free Test 1 | Question: 6
In propositional logic, given $P$ and $P \rightarrow Q$, we can infer ________ $\sim Q$ $Q$ $P \wedge Q$ $\sim P \wedge Q$

In propositional logic, given $P$ and $P \rightarrow Q$, we can infer ________$\sim Q$$Q$$P \wedge Q$$\sim P \wedge Q$

GO Classes

242 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

221

GO 2023 Topic Wise Free Test 1 | Question: 7
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

283 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

222

GO 2023 Topic Wise Free Test 1 | Question: 8
Consider the following Venn diagram: Which one of the following propositions can be used in order to express that the dark gray area on the left of the diagram does not contain any elements? Some Greeks are not mortal. Some Greeks are mortal. All Greeks are mortal. Some non Greeks are non mortal.

Consider the following Venn diagram:Which one of the following propositions can be used in order to express that the dark gray area on the left of the diagram does not co...

GO Classes

186 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

223

GO 2023 Topic Wise Free Test 1 | Question: 9
Consider the following Venn diagram: Which one of the following categorical propositions can be used in order to express that the dark grey area in the center of the diagram does not contain any elements? Some Greeks are not cats. Some non Greeks are non cats. All Greeks are cats. No Greeks are cats.

Consider the following Venn diagram:Which one of the following categorical propositions can be used in order to express that the dark grey area in the center of the diagr...

GO Classes

207 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

224

GO 2023 Topic Wise Free Test 1 | Question: 10
Recall the definitions of valid, satisfiable, and unsatisfiable in the propositional logic. What is the relationship between the above concepts? If a formula $\phi$ is valid then $\phi$ is satisfiable; and if $\phi$ is invalid then $\phi$ is not ... $\phi$ is invalid; and if $\neg \phi$ is satisfiable then $\phi$ is valid.

Recall the definitions of valid, satisfiable, and unsatisfiable in the propositional logic.What is the relationship between the above concepts?If a formula $\phi$ is vali...

GO Classes

155 views

GO Classes asked Dec 5, 2022

8 votes

2 answers

225

GO 2023 Topic Wise Free Test 1 | Question: 11
A set of propositions is called a system specification. System specification is consistent if they do not contain conflicting requirements that could be used to derive a contradiction. When specifications are not consistent, there would be no way ... is retransmitted. Which of the above system specifications are consistent? Only $1$ Only $2$ Both None

A set of propositions is called a system specification.System specification is consistent if they do not contain conflicting requirements that could be used to derive a c...

GO Classes

451 views

GO Classes asked Dec 5, 2022

5 votes

1 answer

226

GO 2023 Topic Wise Free Test 1 | 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?

Two compound propositions are logically equivalent if they have the same truth table.For example, the following two compound propositions are logically equivalent: $\math...

GO Classes

192 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

227

GO 2023 Topic Wise Free Test 1 | Question: 13
Let $p,q,r$ be three propositional variables. Which of the following statements is/are false? $p \rightarrow(q \vee r)) \equiv((p \wedge \neg q) \rightarrow r)$ $(p \wedge q) \vee r \equiv p \wedge(q \vee r)$ If $(p \rightarrow q)$ is FALSE then $(q \rightarrow p)$ is TRUE. If $(p \rightarrow q)$ is TRUE then $(q \rightarrow p)$ is FALSE.

Let $p,q,r$ be three propositional variables.Which of the following statements is/are false?$p \rightarrow(q \vee r)) \equiv((p \wedge \neg q) \rightarrow r)$$(p \wedge q...

GO Classes

140 views

GO Classes asked Dec 5, 2022

2 votes

0 answers

228

GO 2023 Topic Wise Free Test 1 | Question: 14
Which of the following statements is true? The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2} \wedge \dots \wedge S_{n}\rightarrow S$ is satisfiable. The sentence $S$ ... $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is inconsistent.

Which of the following statements is true?The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2} \wedge \dots \wedge S_{n}\rig...

GO Classes

184 views

GO Classes asked Dec 5, 2022

2 votes

0 answers

229

GO 2023 Topic Wise Free Test 1 | Question: 15
Consider a proposition given as: $x \geq 6$, if $x^2 \geq 25 $ and and its proof as: If $x \geq 6$, then $x^2 =x.x \geq 6.6 = 36 \geq 25$ Which of the following is correct with respect to the given proposition and its proof? The ... by assuming what is to be shown The proof is correct and there is nothing wrong $ a$ only $c$ only $a$ and $b$ $b$ only

Consider a proposition given as:$x \geq 6$, if $x^2 \geq 25 $ and and its proof as:If $x \geq 6$, then $x^2 =x.x \geq 6.6 = 36 \geq 25$Which of the following is correct w...

GO Classes

169 views

GO Classes asked Dec 5, 2022

2 votes

0 answers

230

GO 2023 Topic Wise Free Test 1 | Question: 16
If the bank receipt is forged, then Mr. M is liable. If Mr. M is liable, he will go bankrupt. If the bank will loan him money, he will not go bankrupt. The bank will loan him money. Which of the following can be concluded from the above statements? Mr. M is liable The receipt is not forged Mr. M will go bankrupt The bank will go bankrupt

If the bank receipt is forged, then Mr. M is liable.If Mr. M is liable, he will go bankrupt.If the bank will loan him money, he will not go bankrupt.The bank will loan hi...

GO Classes

139 views

GO Classes asked Dec 5, 2022

13 votes

3 answers

231

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 10
Given the truth table of a Binary Operation \$ as follows: $ ... }$ Identify the matching Boolean Expression. $X \$ \neg Y$ $\neg X \$ Y$ $\neg X \$ \neg Y$ none of the options

Given the truth table of a Binary Operation \$ as follows:$$\begin{array}{|l|l|l|l|} \hline {} \text{X} & \text{Y }& \text{X\$Y }\\ \hline \text{1} & \text{0 }& ...

GO Classes

1.0k views

GO Classes asked Dec 5, 2022

0 votes

1 answer

232

Discrete mathematics kenneth rosen
Determine whether the premises If I do not leave my home early or get stuck in a traffic jam, I will be late to my class and get scolded by my teacher , If I am late to my class, I will miss the attendance for the day , and ... today lead to the conclusion Therefore, I have left my home early today . Explain which rules of inference are used for each step.

Determine whether the premises “If I do not leave my home early or get stuck in a traffic jam, I will be late to my class and get scolded by my teacher”, “If I am l...

benzini

747 views

benzini asked Nov 29, 2022

0 votes

1 answer

233

problem from Kenneth Rosen's Discrete Mathematics and its Applications, Section 1.5 - 1.7
Please solve the question. Question: Express each of these system specifications using predicates, quantifiers, and logical connectives. a. Any user with a Gmail account can access services from any Google products. b. ... power failure. d. There is a node whose adjacent nodes are not connected to each other.

Please solve the question. Question: Express each of these system specifications using predicates, quantifiers, and logicalconnectives.a. Any user with a Gmail account ca...

Akif

631 views

Akif asked Nov 27, 2022

0 votes

1 answer

234

Provided by teacher, topic -arguments
Show that: (r → ~ q, r ∪ S, S → ~ q, p → q) ↔ ~ p are inconsistent.

Show that: (r → ~ q, r ∪ S, S → ~ q, p → q) ↔ ~ pare inconsistent.

raj-123

290 views

raj-123 asked Nov 26, 2022

3 votes

0 answers

235

gateforum

h4kr

427 views

h4kr asked Nov 19, 2022

2 votes

0 answers

236

gateforum

h4kr

118 views

h4kr asked Nov 19, 2022

0 votes

0 answers

237

mathe

damz1499

159 views

damz1499 asked Nov 11, 2022

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