1
GATE CSE 2013
MCQ (More than One Correct Answer)
+2
-0.6
Which one of the following is NOT logically equivalent to $$\neg \exists x\left( {\forall y\left( \alpha \right) \wedge \left( {\forall z\left( \beta \right)} \right)} \right)?$$
A
$$\forall x\left( {\exists z\left( {\neg \beta } \right) \to \forall y\left( \alpha \right)} \right)$$
B
$$\forall x\left( {\forall z\left( \beta \right) \to \exists y\left( {\neg \alpha } \right)} \right)$$
C
$$\forall x\left( {\forall y\left( \alpha \right) \to \exists z\left( {\neg \beta } \right)} \right)$$
D
$$\forall x\left( {\exists y\left( {\neg \alpha } \right) \to \exists z\left( {\neg \beta } \right)} \right)$$
2
GATE CSE 2011
+2
-0.6
Which one of the following options is correct given three positive integers $$x, y$$ and $$z$$, and a predicate
$$P\left( x \right) = \neg \left( {x = 1} \right) \wedge \forall y\left( {\exists z\left( {x = y * z} \right) \Rightarrow \left( {y = x} \right) \vee \left( {y = 1} \right)} \right)$$
A
$$P(x)$$ being true means that $$x$$ is a prime number
B
$$P(x)$$ being true means that $$x$$ is a number other than 1
C
$$P(x)$$ is always true irrespective of the value of $$x$$
D
$$P(x)$$ being true means that $$x$$ has exactly two factors other than 1 and $$x$$
3
GATE CSE 2010
+2
-0.6
Suppose the predicate $$F(x,y,t)$$ is used to represent the statements that person $$x$$ can fool person $$y$$ at time $$t$$. Which one of the statements below expresses best the meaning of the formula $$\forall x\exists y\exists t\left( {\neg F\left( {x,y,t} \right)} \right)?$$
A
Everyone can fool some person at some time.
B
No one can fool everyone all the time.
C
Everyone cannot fool some person all the time.
D
No one can fool some person at some time.
4
GATE CSE 2009
+2
-0.6
Which one of the following is the most appropriate logical formula to represent the statement:

"$$Gold\,and\,silver\,ornaments\,are\,precious$$"

The following notations are used:
$$G\left( x \right):\,\,x$$ is a gold ornament.
$$S\left( x \right):\,\,x$$ is a silver ornament.
$$P\left( x \right):\,\,x$$ is precious.

A
$$\forall x\left( {P\left( x \right) \to \left( {G\left( x \right) \wedge S\left( x \right)} \right)} \right)$$
B
$$\forall x\left( {\left( {G\left( x \right) \wedge S\left( x \right)} \right) \to P\left( x \right)} \right)$$
C
$$\exists x\left( {\left( {G\left( x \right) \wedge S\left( x \right)} \right) \to P\left( x \right)} \right)$$
D
$$\forall x\left( {\left( {G\left( x \right) \vee S\left( x \right)} \right) \to P\left( x \right)} \right)$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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