1
GATE CSE 2004
+1
-0.3
Let $$a(x,y)$$, $$b(x,y)$$ and $$c(x,y)$$ be three statements with variables $$x$$ and $$y$$ chosen from some universe. Consider the following statement: $$\left( {\exists x} \right)\left( {\forall y} \right)\left[ {\left( {a\left( {x,\,y} \right) \wedge b\left( {x,\,y} \right)} \right) \wedge \neg c\left( {x,\,y} \right)} \right]$$\$

Which one of the following is its equivalent?

A
$$\left( {\forall x} \right)\left( {\exists y} \right)\left[ {\left( {a\left( {x,\,y} \right) \vee b\left( {x,\,y} \right)} \right) \to c\left( {x,\,y} \right)} \right]$$
B
$$\left( {\exists x} \right)\left( {\forall y} \right)\left[ {\left( {a\left( {x,\,y} \right) \vee b\left( {x,\,y} \right)} \right) \wedge \neg c\left( {x,\,y} \right)} \right]$$
C
$$- \left[ {\left( {\forall x} \right)\left( {\exists y} \right)\left[ {\left( {a\left( {x,\,y} \right) \wedge b\left( {x,\,y} \right)} \right) \to c\left( {x,\,y} \right)} \right]} \right]$$
D
$$- \left[ {\left( {\forall x} \right)\left( {\exists y} \right)\left[ {\left( {a\left( {x,\,y} \right) \vee b\left( {x,\,y} \right)} \right) \to c\left( {x,\,y} \right)} \right]} \right]$$
2
GATE CSE 2002
+1
-0.3
"If X then Y unless Z" is represented by which of the following formulas in propositional logic? (" $$\neg$$ " is negation, " $$\wedge$$ " is conjunction, and " $$\to$$ " is implication)
A
$$\left( {{\rm X} \wedge \neg Z} \right) \to Y$$
B
$$\left( {X \wedge Y} \right) \to \neg Z$$
C
$${\rm X} \to \left( {Y \wedge \neg Z} \right)$$
D
$$\left( {{\rm X} \to Y} \right) \wedge \neg Z$$
3
GATE CSE 2001
+1
-0.3
Consider two well-formed formulas in propositional logic
$$F1:P \Rightarrow \neg P$$
$$F2:\left( {P \Rightarrow \neg P} \right) \vee \left( {\neg P \Rightarrow } \right)$$

Which of the following statements is correct?

A
F1 is satisfiable, F2 is valid
B
F1 is unsatisfiable, F2 is satisfiable
C
F1 is unsatisfiable, F2 is valid
D
F1 and F2 are both satisfiable
4
GATE CSE 1998
+1
-0.3
What is the converse of the following assertion?
I stay only if you go
A
I stay if you go
B
If I stay then you go
C
If you do not go then I do not stay
D
If I do not stay then you go
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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