North Maharashtra University 2008 B.Sc Mathematics S.YBSc MTH – 212 (B) (Computational Algebra) -university question paper

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NORTH MAHARASHTRA UNIVERSITY, JALGAON

(New Syllabus w.e.f. June 2008)
Class : S.Y. B. Sc. Subject : Mathematics
Paper : MTH – 212 (B) (Computational Algebra)
(Calculus of Several Variables)

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1 : ques. of two marks
1) describe reflexive relation and irreflexive relation.
2) describe symmetric and antisymmetric relation.
3) describe transitive closure and symmetric closure of a relation R on
a set A.
4) describe closure and symmetric closure of a relation R on a set A.
5) describe reflexive closure of a relation R on a set A. discuss by an
example.
6) describe rechability relation R* and a relation R8, where R is a
relation on a set A.
7) describe a partition of a set. List all partitions of a set A = {1, 2, 3}.
8) describe Boolean product and Boolean addition of 2 Boolean
matrices.
9) Let A = {1, 2, 3, 4} and R = {(1 , 1) , (1 , 2) , (2 , 3) , (3 , 1) , (4 ,
3) , (3 , 2)}. obtain R(1) , R(2) , R(X) if X = {3, 4}.
10) Let A =
? ? ?
?
?
? ? ?
?
?
1 0 0
0 one 1
1 0 0
, B =
? ? ?
?
?
? ? ?
?
?
1 0 1
0 0 1
1 one 1
. calculate A ? B and A ? B.
2
11) Let A =
? ? ? ?
?
?
? ? ? ?
?
?
0 0 1
1 one 0
0 one 0
1 one 0
, B =
? ? ?
?
?
? ? ?
?
?
1 0 one 1
0 one 1 0
1 0 0 0
. calculate A ?? B.
12) Let A = {a, b, c, d, e}and R be a relation on A and matrix of
relation R is MR =
? ? ? ? ? ?
?
?
? ? ? ? ? ?
?
?
1 0 0 0 0
0 one 1 0 0
0 0 0 one 1
0 0 one 1 0
1 one 0 0 0
. obtain R and its diagraph.
13) If A = {1, 2, 3, 4, 5, 6, 7}and R = {(1 , 2) , (1 , 4) , (2 , 3) , (2 , 5) ,
(3 , 6) , (4 , 7)}then calculate the restriction of R to B = {1, 2, 4, 5}.
14) Let A = {a, b, c, d} and R be the relation on A that has matrix of
relation is MR =
? ? ? ?
?
?
? ? ? ?
?
?
0 one 0 1
1 one 1 0
0 one 0 0
1 0 0 0
. Construct its diagraph. Also obtain
indegree and outdegree for every vertex.
15) obtain the relation and its matrix whose diagraph is provided beneath :
4
1
3
5
2
3
16) For the subsequent diagraph list the indegree and out degree of every
vertex. Also write the corresponding relation :
2 : Multiple option ques. of one marks
1) Let A = {1, 2, 3, 4} , B = {1, 4, 6, 8, 9} and R be a relation from A
to B described by aRb ? b = a2. Then dom(R) = - - - -
a) {1, 2, 3, 4} b) {1, 2, 3}

Earning:   Approval pending.