My question is:

Let A be a finite set with m elements, for some $\displaystyle m\in\mathbb N$. And suppose x is an object that is not a member of A.

Prove, using the definitions, that $\displaystyle A \cup \{x\}$ has m+1 elements.

(All you are told about A is that it has m elements. You need to show that there is a bijection from $\displaystyle \mathbb N_m_+_1$ to $\displaystyle A \cup \{x\}$.)

Any help would be appreciated