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Using the laws of algebra of sets, $(A\cap B')\cup(A'\cup B')$ simplifies to:
A$B'$
B$A'\cap B'$
C$A\cap B'$
D$A'\cup B'$
Answer & Solution
Correct answer: D. $A'\cup B'$
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_
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