1. (a) Let S be the set of all circles in the plane. Define f : S → [0, ∞) by f (C ) = the area of C, for all C ∈ S. Is f injective? Is f surjective? (b) Let T be the set of all circles in the plane...

1. (a) Let S be the set of all circles in the plane. Define f : S → [0, ∞) by f (C ) = the area of C, for all C ∈ S. Is f injective? Is f surjective?

(b) Let T be the set of all circles in the plane that are centered at the origin. Define g : T → [0, ∞) by g(C ) = the area of C, for all C ∈ T. Is g injective? Is g surjective?

2. 10. In each part, find a function f :
 →
 that has the desired properties.

(a) surjective, but not injective

(b) injective, but not surjective

(c) neither surjective nor injective

(d) bijective