Its very urgent please solve the attahed problems till 07-Dec-2007
Thanking you.
What are the graphs for at the top? I can see no use in them.
For 1, consider $\displaystyle f: \mathbb{R} \to \mathbb{R}$
If this is one-to-one then every value of x in the domain produces a distinct value of f(x) in the range. As it is easy to see that f(-x) = f(x), this is not true, so the function is not one to one.
For a function to be onto (ie. surjective) we must use all the values in the codomain (range). The span of the reals includes negative numbers. Can the function produce a negative number?
2. R = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}
I leave it to you to find the inverse relation.
I'm sorry, I don't know what a directed graph is and have no time to look it up. A search on google should tell you the information you need.
-Dan