1
GATE CSE 2015 Set 2
Numerical
+2
-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 ________.
2
GATE CSE 2015 Set 2
Numerical
+2
-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 __________________.
3
GATE CSE 2015 Set 2
+2
-0.6
Which one of the following well formed formulae is a tautology?
A
$$\forall x\,\exists y\,R\left( {x,y} \right) \leftrightarrow \exists y\forall x\,R\left( {x,y} \right)$$
B
$$\left( {\forall x\left[ {\exists y\,R\left( {x,y} \right) \to S\left( {x,y} \right)} \right]} \right) \to \forall x\exists y\,S\left( {x,y} \right)$$
C
$$\left[ {\forall x\,\exists y\,\left( {P\left( {x,y} \right)} \right. \to R\left( {x,y} \right)} \right] \leftrightarrow \left[ {\forall x\,\exists y\,\left( {\neg P\left( {x,y} \right)V\,R\left( {x,y} \right)} \right.} \right]$$
D
$$\forall x\,\forall y\,P\left( {x,y} \right) \to \forall x\forall y\,P\left( {y,x} \right)$$
4
GATE CSE 2015 Set 2
+2
-0.6
In a connected graph, bridge is an edge whose removal disconnects a graph. Which one of the following statements is true?
A
A tree has no bridges
B
A bridge cannot be part of a simple cycle
C
Every edge of a clique with size $$\ge 3$$ is a bridge (A clique is any complete sub-graph of a graph )
D
A graph with bridges cannot have a cycle
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