1
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-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?
A
f and g should both be onto functions
B
f should be onto but g need not be into
C
g should be onto but f need not be onto
D
both f and need not be onto
2
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
3
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
The following is the incomplete operation table of a 4-element group. The last row of the table is
A
$$\matrix{ c & a & e & b \cr }$$
B
$$\matrix{ c & b & a & e \cr }$$
C
$$\matrix{ c & b & e & a \cr }$$
D
$$\matrix{ c & e & a & b \cr }$$
4
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
The inclusion of which of the following sets into

S = { {1, 2}, 1, 2, 3}, {1, 3, 5}, {1, 2, 4},
{1, 2, 3, 4, 5} }
Is necessary and sufficient to make S a complete lattice under the partial order defined by set containment?

A
{1}
B
{1}, {2, 3}
C
{1}, {1, 3}
D
{1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}
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