probability- minimum and maximum value of a union

Question

Suppose that events A and B exist such that P(A)=0.15, P(B)=0.2 . The maximum and minimum possible value for P(not A or not B)

Answer 1

By De Morgan's law, $A^c\cup B^c=(A\cap B)^c$.

With this, $\mathbb{P}(A^c\cup B^c)=\mathbb{P}((A\cap B)^c)=1-\mathbb{P}(A\cap B)$.

Because $0\leq \mathbb{P}(A\cap B)\leq \min\{\mathbb{P}(A),\mathbb{P}(B)\}=0.15$, we have

$0.85\leq\mathbb{P}(A^c\cup B^c)\leq 1$.

These values are reached when $A\subset B$ and $A\cap B=\emptyset$, respectively.