Relations
Questions

2
Doubts on Antisymmetric
Hi Sir,
Doubt may not be up to mark.
Suppose there is a set ‘A’ contains element {1, 2, 3} then
is Rel^n {(1,2)} is antisymmetric?
As per the definition if xRy and yRx then x=y for all x,y belong to A.
but here only xRy is in relation , how it will be antisymmetric. I think there must be at least one ordered pair in the form xRx. I may wrong, please correct me.

definition is in the form of p–>q (yes?)
if yes then read below line
definition is true means p–>q is true (yes ?)
if yes read below line
p–>q is true then either p = false or p=T and q=T.
in your example xRy and yRx is p and x=y is q
substitute (1,2) in the definition
x=1 and y=2
then p will become false, So over all p–>q is true
so definition is true


3
relation

0
Doubt on Irreflexive relations

1
last Statement of this video(1:25:00)
Suppose R = {(1,1)} which is symmetric and transitive but not reflexive.
This may also a counter example of statement 3 ??