Expert: Steve Holleran - 4/13/2007

Question
my questions are about discreate mathematics
Determine whether the given relation defined on the set of positive integers is reflexive, irreflexive, symmetric, antisymmetic, transitive. Justify your answer.
R={(x,y)belonge to R if x=y^2
and the second question is
Let f: RàR defined as f(x)= 4x^2       Check that the function is one-to-one and onto?
plzzz reply me soon.
bye.......  

Answer
Hi Shani,

For the first part of your question, its been too many years since I did abstract algebra, and I can't remember all the steps involved in this problem.

For the second part, its not as bad.  f(x) = 4x^2 is not one-to-one because there are a lot of y values that come from different x's.  For a function to be 1-1, it means that basically, different x's get different y's.  Here, for example, if y = 16, both x = 2 and -2 give this result, so it is not 1-1  (you can also tell because its graph does not pass the "horizontal line test").

It is also not onto, since 4x^2 will always be positive, so none of the negative y's are obtained.

Sorry about part one, but I hope the rest helps out a little.

Steve Holleran