# Questions

• 2

#### Doubts on Antisymmetric

##### mamteshkumar111@gmail.com

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.

• ##### getgatebook

definition is in the form of p–>q (yes?)
if yes then read below line
definition is true means p–>q is true (yes ?)
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

• ##### mamteshkumar111@gmail.com

Thank you sir!
for detailed explanation.

• 3

#### relation

sir among all 6 type of relation. how many relations satisfies ’empty set’ condition also.

• ##### getgatebook

are You asking ” How many properties are satisfied by empty relation?”

yes.

• ##### getgatebook

symmetric and transitive and anti symmetric and Asymmetric and Irreflexive

• 0