Discuss the below:
1. Assuming A,B not equal to no solution, define m1:AxB->A and m2:AxB-> as follows: m1(x,y)=x and m2(x,y)=y. If f: A->B, show that
a) f onto=>m2 |f is onto
b)f one-to-one=>m2 f is one-to-one
2. Assuming f: A->B and g: B->C are bijections, show that (g o f)^-1 = f^-1 o g^-1
3. Find a bijection from A to B when
a) A=[-2,3] and B=[5,14]
b) A=(0,infinity)and B=(-infinity, infinity)
c) A=Natural numbers and B={3,6,9,12,...}