GATE CSE 2005 | GATE CSE Year Wise Previous Years Questions

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GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let R and S be any two equivalence relations on a non-emply set A. Which one of the following statements is TRUE?

$$R\, \cup \,S\,,\,R\, \cap \,S$$ are both equivalence relations

$$R\, \cup \,S\,$$ is an equivalence relations

$$R\, \cap \,S$$ is an equivalence relations

Neither $$R\, \cup \,S\,$$ nor $$R\, \cap \,S$$ is an equivalence relation

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let f: $$\,B \to \,C$$ and g: $$\,A \to \,B$$ be two functions and let h = fog. Given that h is an onto function which one of the following is TRUE?

f and g should both be onto functions

f should be onto but g need not be into

g should be onto but f need not be onto

both f and need not be onto

GATE CSE 2005

MCQ (Single Correct Answer)

-0.3

The set $$\left\{ {1,\,\,2,\,\,4,\,\,7,\,\,8,\,\,11,\,\,13,\,\,14} \right\}$$ is a group under multiplication modulo $$15$$. The inverse of $$4$$ and $$7$$ are respectively:

$$3$$ and $$13$$

$$2$$ and $$11$$

$$4$$ and $$13$$

$$8$$ and $$14$$

GATE CSE 2005

MCQ (Single Correct Answer)

-0.3

Let $$f$$ be a function from a set $$A$$ to a set $$B$$, $$g$$ a function from $$B$$ to $$C$$, and $$h$$ a function from $$A$$ to $$C$$, such that $$h\left( a \right) = g\left( {f\left( a \right)} \right)$$ for all $$a \in A$$. Which of the following statements is always true for all such functions $$f$$ and $$g$$?

$$g$$ is onto $$ \Rightarrow $$ $$h$$ is onto

$$h$$ is onto $$ \Rightarrow $$$$f$$ is onto

$$h$$ is onto $$ \Rightarrow $$ $$g$$ is onto

$$h$$ is onto $$ \Rightarrow $$ $$f$$ and $$g$$ are onto

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