Mathematics 243 – Algebraic Structures Definitions Quiz 3 – September 22, 2006

Your Name:

A) (5) Let f : A → B be a mapping, and let T ⊆ B. What is the definition of the inverse image f^{−1}(T)?

B) (5) Let f : Z → Z be defined by

f(x) = \{ \begin{matrix}2x & if x is odd \\ x − 1 & if x is even \end{matrix}

Is f a permutation of Z? Justify your assertion.