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Recent questions tagged goclasses_wq5
4
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1
GO Classes 2023 | Weekly Quiz 5 | Question: 1
Consider the following atomic propositions: $\text{R}$: It is Raining $\text{S}$ ... is raining, and vice versa It is raining is equivalent to sonu is sick It is raining or sonu is sick but not both
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4
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1
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2
GO Classes 2023 | Weekly Quiz 5 | Question: 2
Let $\text{P}$ be a propositional variable. Which of the following propositions are tautologies? $\text{P}$ $\text{P} \Rightarrow \text{P}$ $(\text{P} \Rightarrow \text{P}) \Rightarrow \text{P}$ $\text{P} \Rightarrow(\text{P} \Rightarrow \text{P})$
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5
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3
GO Classes 2023 | Weekly Quiz 5 | Question: 3
Which of the two following propositions are equivalent in the sense that one can always be substituted for the other one in any proposition without changing its truth value? first proposition $:\text{P} \Rightarrow \text{Q};$ ... $:\neg \text{P};$ second proposition $:\neg \text{P} \vee \text{Q}$
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5
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1
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4
GO Classes 2023 | Weekly Quiz 5 | Question: 4
Let $\text{ KB }$ stand for $\text{ knowledge base }$ which is a set of premises/statements, as mentioned following: Let $\text{S}$ be a propositional formula. Which of the following is $\text{ possible }$? $(\text{KB}\models \text{S})$ ... $(\text{KB} \models \text{S})$ and $(\text{KB} \not \models \neg \text{S})$
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3
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5
GO Classes 2023 | Weekly Quiz 5 | Question: 5
Consider the following popular puzzle. When asked for the ages of her three children, Mrs. Baker says that Alice is her youngest child if Bill is not her youngest child, and that. Alice is not her youngest child if Carl is not ... . Bill is her youngest child. Carl is her youngest child. Information is not sufficient to find out the youngest child.
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5
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6
GO Classes 2023 | Weekly Quiz 5 | Question: 6
Consider the following popular puzzle. A boy and a girl are talking. One of them has black hair, another has white hair. I am a boy said the child with black hair. I am a girl said the child with white hair. At least one of ... lying. Which of them is lying? The boy only The girl only Both of them Information is not sufficient to find out the liar
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2
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7
GO Classes 2023 | Weekly Quiz 5 | Question: 7
Consider the following arguments. $\text{Argument 1:}$ Kerry errs or Myrna fails to show. If Kerry errs, then he does not break the record. Myrna fails to show. Therefore, Kerry does break the record. $\text{Argument 2:}$ If Tasha leaves, ... is true? Only Argument $1$ is valid. Only Argument $2$ is valid. Both Arguments are valid. No Argument is valid.
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2
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8
GO Classes 2023 | Weekly Quiz 5 | Question: 8
Consider the following arguments. $\text{Argument 1:}$ If it does not rain or it is not foggy, then the sailing race will be held, and life-saving demonstrations will go on. If the sailing race is held, then the trophy will be awarded. ... is true? Only Argument $1$ is valid. Only Argument $2$ is valid. Both Arguments are valid. No Argument is valid.
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6
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9
GO Classes 2023 | Weekly Quiz 5 | Question: 9
Consider the following puzzle. Five persons $\text{A, B, C, D, E}$ are in a compartment in a train. $\text{A, C, E}$ are men, and $\text{B, D}$ ... given above, $4$ are true, and $4$ are false. Who is the murderer (Assume exactly one person is the murderer)? A B C D
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10
GO Classes 2023 | Weekly Quiz 5 | Question: 10
Let $\alpha, \beta$ be two propositional formulas. Then which of the following is/are false? If $(\neg \alpha \vee \beta)$ is valid, then $\alpha \models \beta$. If $(\neg \alpha \vee \beta)$ is valid, then $\neg \alpha \models \beta$ ... $\alpha \models \neg \beta$. If $(\neg \alpha \vee \beta)$ is valid, then $\neg \beta \models \neg \alpha$.
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11
GO Classes 2023 | Weekly Quiz 5 | Question: 11
Let $\alpha, \beta$ be two propositional formulas. Which of the following assertions is true? $\alpha$ is valid if and only if True $\models \alpha $. For any $\alpha$, False $\models \alpha$. $\alpha \models \beta $ if and only ... $\alpha \equiv \beta$ if and only if the sentence $(\alpha \Leftrightarrow \beta)$is valid.
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4
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12
GO Classes 2023 | Weekly Quiz 5 | Question: 12
Let $\alpha, \beta $ be two propositional formulas. Which of the following assertions is true? $\alpha \models \beta$ if and only if the sentence $(\alpha \wedge \neg \beta)$ is unsatisfiable. If $\alpha\models \gamma $ ... $\alpha \models(\beta \vee \gamma)$ then $\alpha \models \beta $ or $\alpha \models \gamma $ (or both).
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13
GO Classes 2023 | Weekly Quiz 5 | Question: 13
Consider two formula : $\phi : p\wedge \neg q \rightarrow p\wedge q$ $\psi : \neg p$. Which of the following is/are true? $\phi$ is a logical consequence of the formula $\psi$ $\psi$ is a logical consequence of the formula $\phi$ $\phi$ is a logically equivalent to the formula $\psi$ Neither $\phi$, nor $\psi$, is a logical consequence of the other.
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3
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14
GO Classes 2023 | Weekly Quiz 5 | Question: 14
Which of the following logical consequences are correct? $(p \rightarrow q) |= \neg p \rightarrow \neg q$ $(p \rightarrow q) \wedge \neg q |= \neg p$ $p \rightarrow q \wedge r |= (p \rightarrow q) \rightarrow r$ $p \vee (\neg q \wedge r) |= q \vee \neg r \rightarrow p$
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2
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15
GO Classes 2023 | Weekly Quiz 5 | Question: 15
Let's consider a propositional language where $p$ means Paola is happy , $q$ means Paola paints a picture , $r$ means Renzo is happy . Consider the following sentences and propositional logic formulas : $\text{X} :$ if Paola is happy and paints a picture, then Renzo isn't happy ... $\text{X-1, Y-2, Z-3}$ $\text{X-3, Y-2, Z-1}$
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