Problem ( Proving properties of functions)

Let A,B be two sets. Let f be a function from A to B and let g be a function from B to A. For each of the following functions F1,F2,F3 determine whether the stated property is true or false. Justify your answer, hence, if the property is true then prove it, otherwise, disprove it.

1. The property: F1 is bijective, where F1 is given by: F1:BAAB(y,x)(x,y) If F1 is bijective, then define F1-1.
2. The property: if f and g are bijective then F2 is bijective, where F2 is given by: F2:AAxf-1(g-1(x))
3. The property: if f and g are injective then F3 is bijective, where F3 is given by: F3:ABf(A)g(B)(x,y)(f(x),g(y))