GATE CSE 2005 | GATE CSE Year Wise Previous Years Questions

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

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Which one of the following graphs is NOT planar? GATE CSE 2005 Discrete Mathematics - Graph Theory Question 29 English

GATE CSE 2005

MCQ (Single Correct Answer)

-0.3

Let $$A$$, $$B$$ and $$C$$ be non-empty sets and let $$X = (A - B) - C$$ and $$Y = (A - C) - (B - C)$$

Which one of the following is TRUE?

$$X = Y$$

$$X \subset Y$$

$$Y \subset X$$

None of these

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

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