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

Fill in the Blanks

-0

Maximum number of edges in a planar graph with $$n$$ vertices is _______ .

GATE CSE 1992

Subjective

-0

(a) If G is a group of even order, then
show that there exists an element $$a \ne e$$,
the identifier $$g$$, such that
$${a^2} = e$$

(b) Consider the set of integers $$\left\{ {1,2,3,4,6,8,12,24} \right\}$$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent?
i) Group ii) ring
iii) field iv) lattice
Justify your answer

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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