Show that the relation R in the set R of real numbers , defined as R = {(a,b) : b = a^2} is neither reflexive,nor symmetric nor transitive .

Asked by himanshup8412 | 17th Jul, 2020, 07:28: PM

Expert Answer:

As we know that a not equal to a2 except for the number 1.
So, we have 
straight a not equal to straight a squared space space for all straight a element of straight R minus left curly bracket 1 right curly bracket
Thus space straight R space is space not space reflexive
Let space left parenthesis straight a comma space straight b right parenthesis element of straight R space rightwards double arrow space straight b equals straight a squared
This space does space not space imply space that space straight a equals straight b squared
Thus comma space straight R space is space not space symmetric
Let space left parenthesis straight a comma straight b right parenthesis comma space left parenthesis straight b comma straight c right parenthesis element of straight R
rightwards double arrow straight b equals straight a squared space and space straight c equals straight b squared
rightwards double arrow straight c equals straight b squared equals straight a to the power of 4
This space does space not space imply space straight c equals straight a squared
Thus comma space straight R space is space not space transitive.

Answered by Renu Varma | 21st Jul, 2020, 07:45: PM