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CBSE Class 12-science Answered

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 | 17 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 | 21 Jul, 2020, 07:45: PM

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