GATE CSE 1992 | GATE CSE Year Wise Previous Years Questions

GATE CSE 1992

MCQ (Single Correct Answer)

-0.3

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

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

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

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

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

GATE CSE 1992

Subjective

-0

Uses Modus ponens $$\left( {A,\,\,A \to B\,|\,\, = B} \right)$$ or resolution to show that the following set is inconsistent:

(1) $$Q\left( x \right) \to P\left( x \right)V \sim R\left( a \right)$$
(2) $$R\left( a \right) \vee \sim Q\left( a \right)$$
(3) $$Q\left( a \right)$$
(4) $$ \sim P\left( y \right)$$
where $$x$$ and $$y$$ are universally quantifies variables, $$a$$ is a constant and $$P, Q, R$$ are monadic predicates.

GATE CSE 1992

MCQ (Single Correct Answer)

-0.3

A non-planar graph with minimum number of vertices has

9 edges, 6 vertices

6 edges, 4 vertices

10 edges, 5 vertices

9 edges, 5 vertices

GATE CSE 1992

MCQ (Single Correct Answer)

-0.3

Which of the following is/are tautology?

$$\left( {a \vee b} \right) \to \left( {b \wedge c} \right)$$

$$\left( {a \wedge b} \right) \to \left( {b \vee c} \right)$$

$$\left( {a \vee b} \right) \to \left( {b \to c} \right)$$

$$\left( {a \to b} \right) \to \left( {b \to c} \right)$$

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