1
GATE CSE 2005
+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
+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
3
GATE CSE 2005
+1
-0.3
The following is the Hasse diagram of the poset $$\left[ {\left\{ {a,b,c,d,e} \right\}, \prec } \right]$$

The poset is:

A
not a lattice
B
a lattice but not a distributive lattice
C
a distributive lattice but not a Boolean algebra
D
a Boolean algebra
4
GATE CSE 2004
+1
-0.3
Consider the binary relation: $$S = \left\{ {\left( {x,y} \right)|y = x + 1\,\,and\,\,x,y \in \left\{ {0,1,2,...} \right\}} \right\}$$

The reflexive transitive closure of $$S$$ is

A
$$\left\{ {\left( {x,y} \right)|y > x\,\,\,and\,\,\,x,y \in \left\{ {0,1,2,.....} \right\}} \right\}$$
B
$$\left\{ {\left( {x,y} \right)|y \ge x\,\,\,and\,\,\,x,y \in \left\{ {0,1,2,.....} \right\}} \right\}$$
C
$$\left\{ {\left( {x,y} \right)|y < x\,\,\,and\,\,\,x,y \in \left\{ {0,1,2,.....} \right\}} \right\}$$
D
$$\left\{ {\left( {x,y} \right)|y \le x\,\,\,and\,\,\,x,y \in \left\{ {0,1,2,.....} \right\}} \right\}$$
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