1
GATE CSE 2014 Set 3
+2
-0.6
The CORRECT formula for the sentence, "not all rainy days are cold" is
A
$$\forall d\left( {Rainy\left( d \right) \wedge \sim Cold\left( d \right)} \right)$$
B
$$\forall d\left( { \sim Rainy\left( d \right) \to Cold\left( d \right)} \right)$$
C
$$\exists d\left( { \sim Rainy\left( d \right) \to Cold\left( d \right)} \right)$$
D
$$\exists d\left( {Rainy\left( d \right) \wedge \sim Cold\left( d \right)} \right)$$
2
GATE CSE 2014 Set 1
+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
$$\left( { \sim \left( {p \leftrightarrow q} \right) \wedge r} \right) \wedge \left( {p \wedge q \wedge \sim r} \right)$$
3
GATE CSE 2013
+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
$$\neg \exists x\left( {F\left( x \right) \wedge P\left( x \right)} \right)$$
4
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
$$\forall x\left( {\exists y\left( {\neg \alpha } \right) \to \exists z\left( {\neg \beta } \right)} \right)$$
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
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