1
GATE CSE 2005
MCQ (Single Correct Answer)
+1
-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 $$g$$?
A
$$g$$ is onto $$ \Rightarrow $$ $$h$$ is onto
B
$$h$$ is onto $$ \Rightarrow $$$$f$$ is onto
C
$$h$$ is onto $$ \Rightarrow $$ $$g$$ is onto
D
$$h$$ is onto $$ \Rightarrow $$ $$f$$ and $$g$$ are onto
2
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following graphs is NOT planar? GATE CSE 2005 Discrete Mathematics - Graph Theory Question 29 English
A
G1
B
G2
C
G3
D
G4
3
GATE CSE 2005
MCQ (Single Correct Answer)
+1
-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?

A
$$X = Y$$
B
$$X \subset Y$$
C
$$Y \subset X$$
D
None of these
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-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?
A
$$R\, \cup \,S\,,\,R\, \cap \,S$$ are both equivalence relations
B
$$R\, \cup \,S\,$$ is an equivalence relations
C
$$R\, \cap \,S$$ is an equivalence relations
D
Neither $$R\, \cup \,S\,$$ nor $$R\, \cap \,S$$ is an equivalence relation
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