#Gate2003
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Syedarshadali asked Jun 29, 2017 • closed Jun 29, 2017 by Arjun

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Kathleen asked Sep 16, 2014

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GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations $I_1$ and $I_2$. $\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]$ $I_1$ : Domain: ... I_1\) does not Neither $I_1$ nor $I_2$ satisfies $\alpha$ Both $I_1$ and $I_2$ satisfies $\alpha$

Consider the following formula and its two interpretations $I_1$ and $I_2$.\(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg...

Kathleen

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Kathleen asked Sep 16, 2014

59 votes

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Kathleen asked Sep 16, 2014

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GATE CSE 2003 | Question: 32
Which of the following is a valid first order formula? (Here $\alpha$ and $\beta$ are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$

Which of the following is a valid first order formula? (Here $\alpha$ and $\beta$ are first order formulae with $x$ as their only free variable)$((∀x)[α] ⇒ (∀x...

Kathleen

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Kathleen asked Sep 16, 2014

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USharma02 asked Dec 24, 2023

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Mathematical Logic: Which of the following is a logical consequence of $∀x(p(x)∨q(x))$
The following question is on the NPTEL archive of Assignment 2 of Discrete Mathematics Course,(Link : assessment id-15 (nptel.ac.in)) . I am not able to get how the answer is given option A but I am getting B, C and D. I have also attached my reasoning below. Let me know If I am missing something.

The following question is on the NPTEL archive of Assignment 2 of Discrete Mathematics Course,(Link : assessment id-15 (nptel.ac.in)) . I am not able to get howthe answe...

USharma02

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USharma02 asked Dec 24, 2023

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Ray Tomlinson asked Nov 29, 2023

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Made Easy Test Series 2024
anyone explain why option B is wrong?

anyone explain why option B is wrong?

Ray Tomlinson

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Ray Tomlinson asked Nov 29, 2023

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