1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Let S = {1, 2, 3,....., m} , m > 3. Let $${X_1},\,....,\,{X_n}$$ be subsets of S each of size 3. Define a function f from S to the set of natural numbers as, f (i) is the number of sets $${X_j}$$ that contain the element i. That is $$f(i) = \left\{ {j\left| i \right.\,\, \in \,{X_j}} \right\}\left| . \right.$$

Then $$\sum\limits_{i - 1}^m {f\,(i)} $$ is

A
3m
B
3n
C
2m + 1
D
2n + 1
2
GATE CSE 2006
MCQ (Single Correct Answer)
+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
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 35 English Option 1
B
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 35 English Option 2
C
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 35 English Option 3
D
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 35 English Option 4
3
GATE CSE 2005
MCQ (Single Correct Answer)
+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!
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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