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:** $n! = n \cdot (n - 1)!$.
$n!$ is defined inductively by $0!=1$ and $n!=n\cdot(n-1)!$ for $n\geqslant 1$. Hence
$$n! - (n-1)! = n\cdot(n-1)! - (n-1)! = (n-1)(n-1)! $$