[SOLVED] A few intro to advanced math topics
Ok, so I have a few problems that I need to work on and have some progress made by Monday. The problem is that I need to work 30+ hours this weekend. So thanks in advance to anyone who assissts in solving, offers some advice, or views this topic
1) Let f: X--> Y and let A,B be subsets of Y. Prove that f^-1(A) - f^-1(B)= f^-1 (A-B).
Kind of a fun problem. Just show containment both ways.
2) Let f: X-->A and g: Y-->B. Define a function f x g by (f x g)(x,y)= (f(x),g(y)) for all (x,y) as elements in X x Y.
note that f x g is f cross g, not f times g.
Prove the following
a) If f and g are one-ton-one, then f x g is one-to-one.
b) If f maps onto A and g maps onto B then f x g maps on A x B
3) True or False? If false give a specific counter example (So indicate exactly what the sets and functions involved are) Assume f: X --> Y and
g: Y--> Z
a) If F^-1(Y) = X, then f maps onto Y
b) If g composed with f maps onto Z, then f maps onto Y
Again, thank you very much