1
GATE CSE 1995
Subjective
+5
-0
Let $${G_1}$$ and $${G_2}$$ be subgroups of a group $$G$$.
(a) Show that $${G_1}\, \cap \,{G_2}$$ is also a subgroup of $$G$$.
(b) $${\rm I}$$s $${G_1}\, \cup \,{G_2}$$ always a subgroup of $$G$$?
(a) Show that $${G_1}\, \cap \,{G_2}$$ is also a subgroup of $$G$$.
(b) $${\rm I}$$s $${G_1}\, \cup \,{G_2}$$ always a subgroup of $$G$$?
2
GATE CSE 1992
Subjective
+5
-0
(a) If G is a group of even order, then
show that there exists an element $$a \ne e$$,
the identifier $$g$$, such that
$${a^2} = e$$
show that there exists an element $$a \ne e$$,
the identifier $$g$$, such that
$${a^2} = e$$
(b) Consider the set of integers $$\left\{ {1,2,3,4,6,8,12,24} \right\}$$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent?
i) Group ii) ring
iii) field iv) lattice
Justify your answer
Questions Asked from Set Theory & Algebra (Marks 5)
Number in Brackets after Paper Indicates No. of Questions
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude