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

1. By De Morgan's law $(A\cup B)'=A'\cap B'$ and $(A\cap B)'=A'\cup B'$. 2. The expression becomes $(A'\cap B')\cap(A'\cup B')$. 3. Here $A'\cap B'$ is a subset of $A'\cup B'$, so the intersection returns the smaller set. 4. Hence the result is $A'\cap B'$. 5. Answering $B$ applies De Morgan's law to only one bracket and then cancels wrongly. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 5: Sets_