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Recent questions tagged goclasses2024_wq5
5
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2
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1
GO Classes Weekly Quiz 5 | Propositional Logic | 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 ... go to the shopping mall. If it is not raining then Kareena and Parineeti do not go to the shopping mall.
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6
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3
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2
GO Classes Weekly Quiz 5 | Propositional Logic | 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
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3
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3
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3
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 3
Select the proposition that is a tautology. $(p \wedge q) \rightarrow \neg p$ $(p \vee q) \rightarrow p$ $(p \wedge q) \leftrightarrow p$ $(p \wedge q) \rightarrow p$
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5
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1
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4
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 4
Select the proposition that is a contradiction. $\neg(p \vee q) \wedge p$ $(p \vee q) \wedge p$ $(\neg p \wedge q) \leftrightarrow p$ $(\neg p \wedge q) \rightarrow p$
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6
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5
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 5
In propositional logic, given $P$ and $P \rightarrow Q$, we can infer ________ $\sim Q$ $Q$ $P \wedge Q$ $\sim P \wedge Q$
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9
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3
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6
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 6
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 $S$ is a logical ... $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is inconsistent.
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11
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7
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 7
If $F_1, F_2$ and $F_3$ are propositional formulae/expressions, over same set of propositional variables, such that $F_1\wedge F_2\rightarrow F_3$ is a contradiction, then which of the following is/are necessarily true? Both $F_1$ and ... $F_3$ is a contradiction $F_1,\;F_2$ and $F_3$ all are contradictions.
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29
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2
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8
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 8
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 a ... Craig interpolant for $\varphi$ and $\psi?$ $\varphi$ itself $q \vee s$ $q \vee r$ $\neg q \wedge s$
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17
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1
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9
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 9
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 $\phi$ ... not satisfiable, then $\phi$ is invalid; and if $\neg \phi$ is satisfiable then $\phi$ is valid.
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14
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4
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10
GO Classes Weekly Quiz 5 | 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 : $P \vee R$ $P \vee S$ $Q \vee R$ $Q \vee S$
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22
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1
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11
GO Classes Weekly Quiz 5 | Propositional Logic | 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 ... retransmitted. Which of the above system specifications are consistent? Only $1$ Only $2$ Both None
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27
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12
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?
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3
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13
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 13
Let $p,q,r$ be three propositional variables. Which of the following statements is/are false? $p \rightarrow(q \vee r)) \equiv((p \wedge \neg q) \rightarrow r)$ $(p \wedge q) \vee r \equiv p \wedge(q \vee r)$ ... is FALSE then $(q \rightarrow p)$ is TRUE. If $(p \rightarrow q)$ is TRUE then $(q \rightarrow p)$ is FALSE.
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7
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14
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 14
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 ... assuming what is to be shown The proof is correct and there is nothing wrong $ a$ only $c$ only $a$ and $b$ $b$ only
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9
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1
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15
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 15
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
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49
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6
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16
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 16
If $\text{F1, F2}$ and $\text{F3}$ are propositional formulae/expressions, over some set of propositional variables, such that $\mathrm{F} 1 \vee F 2 \rightarrow \mathrm{F} 3$ is a contradiction, then which of the following is/are ... is a tautology. $\text{F3}$ is a contradiction. $\text{F1} \mathrm{v} \text{F2}$ is a tautology.
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