The Venn diagram method will work fine.
Draw the usual two intersecting ovals, and label them $A$ and $B$.
You can see $A\cap B$ in the picture. It is the region in common between $A$ and $B$. We are told that $\Pr(A\cap B)=0.2$. Write $0.2$ in the region in common between $A$ and $B$.
The event (set) $(A\cup B)^c$ is the complement of the union of $A$ and $B$. So it is the region which is outside both $a$ and $B$, it is the rest of the world. The probability of that is $0.5$. Write $0.5$ somewhere in that region.
We want the probability of being in $A$ or $B$ but not in both. That region is made up of two parts, neither of which has yet been counted in. Call the probability of being in that split region $x$. Then
because the probability of landing somewhere is $1$. Now we can find $x$.
Another way: Because the probability of the "rest of the world" is $0.5$, the probability of $A\cupB$ is $1-0.5$, which is $0.5$.
The part in both $A$ and $B$ has probability $0.2$. So the probability of being in $A$ or $B$ but not both is $0.5-0.2$.