Question: Is it true?

$X= Y \cup Z$, $M$ is a subset of $Y \cap Z$. Suppose that $M$ is open in $Y$ and $M$ is open in $Z$ then $M$ is open in $X$.

Answer: 
**Hint:** $n! = n \cdot (n - 1)!$.
$$n!-(n-1)!=n(n-1)!-(n-1)!=(n-1)!\left( n-1 \right) $$