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

2
Doubt on Irreflexive relations
Sir,Suppose i have a set A={1,2,3} and a relation R on Set A is given as {(1,1,),(2,2)},now this is clearly not reflexive,can we say that this relation is irreflexive because not all the elements that are required to satisfy the reflexive property are present here

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 ?? 
2
10:53
aRb, you are mapping only 1R1,2R2, but why not from 1R2, 1R3 like this then it wont be reflexive, please clear this?

2
@1:15:00 #no. of asymmetric realtion
Sir
#No of asymmetric relation should be=( 3^ (n^2n/2) )1
because here ( 3^ (n^2n/2) ) we are considering a relation which is empty relation and empty relation is by default symmetric so we have to remove this case…… 
1
#no of irreflexive relation