GATE CSE 2001 | Mathematical Logic Question 51 | Discrete Mathematics

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

If I do not stay then you go

GATE CSE 1993

MCQ (Single Correct Answer)

-0.3

The proposition $$p \wedge \left( { \sim p \vee q} \right)$$ is

a tautology

$$ \Leftrightarrow \left( {p \wedge q} \right)$$

$$ \Leftrightarrow \left( {p \vee q} \right)$$

a contradiction

GATE CSE 1992

MCQ (Single Correct Answer)

-0.3

Which of the following predicate calculus statements is/are valid?

$$\left( {\forall \,x} \right){\rm P}\left( x \right) \vee \left( {\forall \,x} \right)Q\left( x \right) \to \left( {\forall \,x} \right)$$
$$\left\{ {{\rm P}\left( x \right) \vee Q\left( x \right)} \right\}$$

$$\left( {\exists \,x} \right){\rm P}\left( x \right) \wedge \left( {\exists \,x} \right)Q\left( x \right) \to \left( {\exists \,x} \right)$$
$$\left\{ {{\rm P}\left( x \right) \wedge Q\left( x \right)} \right\}$$

$$\left( {\forall \,x} \right)\,\left\{ {{\rm P}\left( x \right) \vee Q\left( x \right)} \right\} \to \left( {\forall \,x} \right)\,\,$$
$${\rm P}\left( x \right) \vee \left( {\forall \,x} \right)\,\,Q\left( x \right)$$

$$\left( {\exists \,x} \right)\,\,\left\{ {{\rm P}\left( x \right) \vee Q\left( x \right)} \right\} \to \sim \left( {\forall \,x} \right)\,\,$$
$$\,{\rm P}\left( x \right) \vee \left( {\exists \,x} \right)Q\left( x \right)$$