Science:Math Exam Resources/Courses/MATH220/December 2011/Question 04/Statement

Let ƒ: A → B be a function. If C ⊆ A, define

$f(C)=\{f(x)\mid x\in C\}$

Prove that if ƒ is injective, then

$f(C\cap D)=f(C)\cap f(D)\text{for all sets }C,D\subseteq A$