GATE CSE 2015 Set 2 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.6

In a connected graph, bridge is an edge whose removal disconnects a graph. Which one of the following statements is true?

A tree has no bridges

A bridge cannot be part of a simple cycle

Every edge of a clique with size $$ \ge 3$$ is a bridge (A clique is any complete sub-graph of a graph )

A graph with bridges cannot have a cycle

GATE CSE 2015 Set 2

Numerical

-0

The number of onto functions (subjective functions) from set $$X = \left\{ {1,2,3,4} \right\}$$ to set $$Y = \left\{ {a,b,c} \right\}$$ is __________________.

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GATE CSE 2015 Set 2

Numerical

-0

Let $$X$$ and $$Y$$ denote the sets containing $$2$$ and $$20$$ distinct objects respectively and $$𝐹$$ denote the set of all possible functions defined from $$X$$ to $$Y$$. Let $$f$$ be randomly chosen from $$F.$$ The probability of $$f$$ being one-to-one is ________.

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GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.6

Which one of the following well formed formulae is a tautology?

$$\forall x\,\exists y\,R\left( {x,y} \right) \leftrightarrow \exists y\forall x\,R\left( {x,y} \right)$$

$$\left( {\forall x\left[ {\exists y\,R\left( {x,y} \right) \to S\left( {x,y} \right)} \right]} \right) \to \forall x\exists y\,S\left( {x,y} \right)$$

$$\left[ {\forall x\,\exists y\,\left( {P\left( {x,y} \right)} \right. \to R\left( {x,y} \right)} \right] \leftrightarrow \left[ {\forall x\,\exists y\,\left( {\neg P\left( {x,y} \right)V\,R\left( {x,y} \right)} \right.} \right]$$

$$\forall x\,\forall y\,P\left( {x,y} \right) \to \forall x\forall y\,P\left( {y,x} \right)$$

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