Re: 2006 dse q31

Posted by Priyanka kothari on Aug 05, 2011; 12:53am
URL: http://discussion-forum.276.s1.nabble.com/2006-dse-q31-tp6643980p6654907.html

Hi!

 few definition try to understand them :(a) Reflexivity: for every x belongs to S : (x; x) belongs to R
(b) Completeness:for every x; y belongs to S : x 6= y ) (x; y) belongs to R or (y; x) belongs to R
(c) Transitivity: for every x; y; z belongs to S : ((x; y) belongs to R and (y; z) belongs to R) ) (x; z) belongs to R
(d) Symmetry: for every x; y belongs to S : (x; y) belongs to R ) (y; x) belongs to R
(e) Anti-symmetry: for every x; y belongs to S : ((x; y) belongs to R and (y; x) belongs to R) ) x = y
(f) Asymmetry: for every x; y belongs to S : (x; y) 2 R ) (y; x) does not belong to R
(g) Negative transitivity: for every x; y; z belongs to S : ((x; y) does not belong to R and (y; z) does not belong to R) ) (x; z) does not belong to R
(h) Equivalence: Relation which is symmetric, reflexive and transitive.

 do following question and explain your ans as well
1)S = {1,2,3}
 a)A ={(1,1), (2,2).(3,1)} determine if set A is reflexive(R/NR), transitive(T/NT) and    symmetric(S/NS)
 b) A = {(1,1),(2,1),(2,2),(3,3),(3,1)} determine if set S is reflexive(R/NR), transitive(T/NT)  and  symmetric(S/NS)

2)determine if set S is reflexive(R/NR), transitive(T/NT) and  symmetric(S/NS)        {N=not}
if S is the set  of all pairs of real nos. s.t
a) x<=y
B)x<y
C) x< lyl  
d)x^2 + y^2 = 1
e)x^2 + y^2 <0
f) x^2 + x=y^2 +y