Relations

Asked by  | 6th Apr, 2009, 03:38: PM

Expert Answer:

(i) R is not reflexive.

a is not less than or equal to a2 for all a R.

e.g fractions like 1/3 is not less than or equal 1/9

(ii) R is not symmetric since if a≤ b2 then b is not less than or equal to a2

eg 2 ≤ 52 but  5 is not less than 22

(iii) R is not transitive, If a≤ b2, b≤ c2 then a is not necesaarily less than c2

eg 2 ≤ (-2)2 ,  -2≤ (-1)2

But 2 is not less than (-1)2

So R is neither reflexive nor symmetric nor transitive.

Answered by  | 14th Apr, 2009, 10:17: AM

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