Using the laws of algebra of sets, $(A\cap B')\cup(A'\cup B')$ simplifies to:

1. Note $A'\cup B'$ already contains every element outside $A$ or outside $B$. 2. The set $A\cap B'$ consists of elements in $A$ but not in $B$, so each of them lies in $B'$ and therefore in $A'\cup B'$. 3. A union with one of its own subsets changes nothing: $(A\cap B')\cup(A'\cup B')=A'\cup B'$. 4. Collapsing the answer to $B'$ discards the $A'$ part of the union. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 5: Sets_