1
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!
2
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
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 2004
+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
$$\matrix{ c & e & a & b \cr }$$
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
EXAM MAP
Joint Entrance Examination