1
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following propositional logic formulas is TRUE when exactly two of $$p, q,$$ and $$r$$ are TRUE?
A
$$\left( {\left( {p \leftrightarrow q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$
B
$$\left( { \sim \left( {p \leftrightarrow q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$
C
$$\left( {\left( {p \to q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$
D
$$\left( { \sim \left( {p \leftrightarrow q} \right) \wedge r} \right) \wedge \left( {p \wedge q \wedge \sim r} \right)$$
2
GATE CSE 2013
MCQ (Single Correct Answer)
+2
-0.6
What is the logical translation of the following statement?
"None of my friends are perfect."
A
$$\exists x\left( {F\left( x \right) \wedge \neg P\left( x \right)} \right)$$
B
$$\exists x\left( {\neg F\left( x \right) \wedge P\left( x \right)} \right)$$
C
$$\exists x\left( {\neg F\left( x \right) \wedge \neg P\left( x \right)} \right)$$
D
$$\neg \exists x\left( {F\left( x \right) \wedge P\left( x \right)} \right)$$
3
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
$$\forall x\left( {\exists y\left( {\neg \alpha } \right) \to \exists z\left( {\neg \beta } \right)} \right)$$
4
GATE CSE 2011
MCQ (Single Correct Answer)
+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 $$x$$
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