GATE CSE 2004 | Mathematical Logic Question 45 | Discrete Mathematics

GATE CSE 2004

MCQ (Single Correct Answer)

-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?

$$\left( {\forall x} \right)\left( {\exists y} \right)\left[ {\left( {a\left( {x,\,y} \right) \vee b\left( {x,\,y} \right)} \right) \to c\left( {x,\,y} \right)} \right]$$

$$\left( {\exists x} \right)\left( {\forall y} \right)\left[ {\left( {a\left( {x,\,y} \right) \vee b\left( {x,\,y} \right)} \right) \wedge \neg c\left( {x,\,y} \right)} \right]$$

$$ - \left[ {\left( {\forall x} \right)\left( {\exists y} \right)\left[ {\left( {a\left( {x,\,y} \right) \wedge b\left( {x,\,y} \right)} \right) \to c\left( {x,\,y} \right)} \right]} \right]$$

$$ - \left[ {\left( {\forall x} \right)\left( {\exists y} \right)\left[ {\left( {a\left( {x,\,y} \right) \vee b\left( {x,\,y} \right)} \right) \to c\left( {x,\,y} \right)} \right]} \right]$$

GATE CSE 2002

MCQ (Single Correct Answer)

-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)

$$\left( {{\rm X} \wedge \neg Z} \right) \to Y$$

$$\left( {X \wedge Y} \right) \to \neg Z$$

$${\rm X} \to \left( {Y \wedge \neg Z} \right)$$

$$\left( {{\rm X} \to Y} \right) \wedge \neg Z$$

GATE CSE 2001

MCQ (Single Correct Answer)

-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?

F1 is satisfiable, F2 is valid

F1 is unsatisfiable, F2 is satisfiable

F1 is unsatisfiable, F2 is valid

F1 and F2 are both satisfiable

GATE CSE 1998

MCQ (Single Correct Answer)

-0.3

What is the converse of the following assertion?
I stay only if you go

I stay if you go

If I stay then you go

If you do not go then I do not stay