##### Set theory and algebra

Consider the set S = {a, b} and ‘L’ be a binary relation such that L = {all binary relations except reflexive relation set S}. The number of relation which are symmetric _______.

shivani
4 Oct 2017 06:07 pm

all binary relations except reflexive relation set S involves removing all diagonal elements , then we are left with (n2 - n) elements for symmetricity if (a,b) is present then it is must that (b,a) should be present , so we have got 2(n(n-1)/2)

Shri Shivi
4 Oct 2017 06:57 pm

yes from this expression only I got 2  but the given ans is 6

shivani
4 Oct 2017 07:22 pm

now you can judge answer better

gaurav singh
5 Oct 2017 10:44 am
• {aa},{bb},{ab,ba},{aa,ab,ba},{bb,ab,ba},{} are symmetric but not reflexive.hence 6 would be the answer. IN 2^n*n-1/2 case you are completely ignoring diagonal elements but we can take some diaonal elements not all in the case.
shivani
5 Oct 2017 01:28 pm

Binary relation on set S = SxS
so, how could you get {aa},{bb},{ab,ba},{aa,ab,ba},{bb,ab,ba},{}
provide some source for validity