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
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