# Math Help - need help with 2 proofs

1. ## need help with 2 proofs

Prove: If |A| = n and A is equinumerous to B, then |B| = n

Prove: Let A and B be finite sets. Conjecture a formula for |A U B| in the case that A n B doesn't equal the empty set

2. Originally Posted by dbhakta
Prove: If |A| = n and A is equinumerous to B, then |B| = n
If $|A|=n$ it means there is a bijection $\theta : A\mapsto n$, and $|A|=|B|$ means there is a bijection $\eta: A\mapsto B$. Thus, the mapping $\theta \circ \eta^{-1}$ will be a bijection from $B$ to $n$.

Prove: Let A and B be finite sets. Conjecture a formula for |A U B| in the case that A n B doesn't equal the empty set
If $|A|=n$ and $|B|=m$ then $|A\cup B| \leq n+m$ and we have equality when $A\cap B=\emptyset$.