GATE CSE 1993 | Mathematical Logic Question 63 | Discrete Mathematics

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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?

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

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

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

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

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