1
GATE CSE 2006
+2
-0.6
Consider the set S = {a, b, c, d}. Consider the following 4 partitions $$\,{\pi _1},\,{\pi _2},\,{\pi _3},\,{\pi _4}$$ on $$S:\,{\pi _1} = \left\{ {\overline {a\,b\,c\,d} } \right\},\,{\pi _2} = \left\{ {\overline {a\,b\,} ,\,\overline {c\,d} } \right\},\,{\pi _3} = \left\{ {\overline {a\,b\,c\,} ,\,\overline d } \right\},\,{\pi _4} = \left\{ {\overline {a\,} ,\,\overline b ,\,\overline c ,\,\overline d } \right\}.$$ Let $$\prec$$ be the partial order on the set of partitions $$S' = \{ {\pi _1},\,{\pi _2},\,{\pi _3},\,{\pi _4}\}$$ defined as follows: $${\pi _i} \prec \,\,{\pi _j}$$ if and only if $${\pi _i}$$ refines $${\pi _j}$$. The poset diagram for $$(S',\, \prec )$$ is
A
B
C
D
2
GATE CSE 2005
+2
-0.6
Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for any two subsets $${S_1}$$ and $${S_2}$$ in C, either $${S_1}\, \subset \,{S_2}$$ or $${S_2}\, \subset \,{S_1}$$. What is the maximum cardinality of C?
A
n
B
n + 1
C
$${2^{n - 1}}\, + \,1$$
D
n!
3
GATE CSE 2005
+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
4
GATE CSE 2005
+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
GATE CSE Subjects
EXAM MAP
Medical
NEET