Recent questions tagged propositional-logic

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DRDO CSE 2022 Paper 1 | Question: 12
Given two propositions $P$ and $Q$. "if $P$ then $Q$" denoted by $P \rightarrow Q$ is called Implication. Such implication and its ____________ are logically equivalent.

Given two propositions $P$ and $Q$. "if $P$ then $Q$" denoted by $P \rightarrow Q$ is called Implication. Such implication and its ____________ are logically equivalent.

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admin asked Dec 15, 2022

0 votes

2 answers

122

# 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 ?

540 views

Aditi Thakur asked Dec 7, 2022

2 votes

0 answers

123

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...

148 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

124

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...

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GO Classes asked Dec 5, 2022

2 votes

0 answers

125

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

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GO Classes asked Dec 5, 2022

2 votes

0 answers

126

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$

135 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

127

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$

173 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

128

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$

246 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

129

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...

284 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

130

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...

158 views

GO Classes asked Dec 5, 2022

8 votes

2 answers

131

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...

464 views

GO Classes asked Dec 5, 2022

5 votes

1 answer

132

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...

196 views

GO Classes asked Dec 5, 2022

2 votes

1 answer

133

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...

144 views

GO Classes asked Dec 5, 2022

2 votes

0 answers

134

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...

185 views

GO Classes asked Dec 5, 2022

2 votes

0 answers

135

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...

170 views

GO Classes asked Dec 5, 2022

2 votes

0 answers

136

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...

140 views

GO Classes asked Dec 5, 2022

15 votes

3 answers

137

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 }& ...

1.2k views

GO Classes asked Dec 5, 2022

0 votes

1 answer

138

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.

299 views

raj-123 asked Nov 26, 2022

0 votes

1 answer

139

Translate the given statement into propositional logicexpressions:“A man qualifies for the marathon if his best previous time is less than 3 hours and a woman qualifies for the marathon if her best previous time is less than 3.5 hours.

722 views

VASEEMUN asked Oct 29, 2022

0 votes

0 answers

140

UGC NET CSE | October 2022 | Part 1 | Question: 85
Consider $\alpha, \beta, \gamma$ as logical variables. Identify which of the following represents correct logical equivalence : (A) $(\alpha \wedge(\beta \vee \gamma)) \equiv((\alpha \wedge \beta) \vee(\alpha \wedge \gamma))$ ... options given below : (A) and (D) only (B) and (C) only, (A) and (C) only (B) and (D) only

Consider $\alpha, \beta, \gamma$ as logical variables. Identify which of the following represents correct logical equivalence :(A) $(\alpha \wedge(\beta \vee \gamma)) \eq...

190 views

admin asked Oct 23, 2022

0 votes

3 answers

141

Predicate Translation
S(x): x is a Student P(x): x is a Professor A(x, y): x has asked a question to y Domain not given, so we have to think about default domain Q1) Translate There is a student who has asked every professor a question Q2) Translate ... a professor who has been asked a question by every student Q4) Translate There is a student who has been asked a question by every professor

S(x): x is a StudentP(x): x is a ProfessorA(x, y): x has asked a question to yDomain not given, so we have to think about default domainQ1) Translate “There is a studen...

685 views

prithatiti asked Sep 6, 2022

2 votes

2 answers

142

GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 4
How many rows appear in a truth table for this compound proposition? $p \rightarrow \neg p$

How many rows appear in a truth table for this compound proposition?$p \rightarrow \neg p$

477 views

GO Classes asked May 2, 2022

4 votes

4 answers

143

GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 5
How many rows appear in a truth table for this compound proposition? $(p \wedge r \wedge t) \leftrightarrow (q \wedge t)$

How many rows appear in a truth table for this compound proposition?$(p \wedge r \wedge t) \leftrightarrow (q \wedge t)$

657 views

GO Classes asked May 2, 2022

8 votes

3 answers

144

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 1
Let $p$ be the statement Maria learns discrete mathematics and $q$ the statement Maria will find a good job. Which of the following English Statement expresses the statement $p \rightarrow q?$ If Maria learns discrete ... good job. For Maria to get a good job, it is sufficient for her to learn discrete mathematics.

Let $p$ be the statement “Maria learns discrete mathematics” and $q$ the statement “Maria will find a good job.” Which of the following English Statement expresse...

1.8k views

GO Classes asked May 2, 2022

12 votes

3 answers

145

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...

1.3k views

GO Classes asked May 2, 2022

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