In: Advanced Math
Consider the following relations:
R1 = {(a, b) ∈
R2 ∣ a > b}, the
greater than relation
R2 = {(a, b) ∈
R2 ∣ a ≥ b}, the
greater than or equal to relation
R3 = {(a, b) ∈
R2 ∣ a < b}, the
less than relation
R4 = {(a, b) ∈
R2 ∣ a ≤ b}, the less
than or equal to relation
R5 = {(a, b) ∈
R2 ∣ a = b}, the
equal to relation
R6 = {(a, b) ∈
R2 ∣ a ≠ b}, the
unequal to relation
For these relations on the set of real numbers, find
R2∘R1
R2∘R2
R3∘R5
R4∘R1
R5∘R3
R3∘R6
R4∘R6
R6∘R6
If you have any doubts please ask me in comments ...
Here i used general definiton of composition of relations....