alleryIf $B=\{x:2\le x\le5\}$, then its complement $B'$ is:
A$\{x:x<2$ or $x>5\}$
B$\{x:2<x<5\}$
C$\{x:x\le2$ or $x\ge5\}$
D$\{x:x>2$ and $x<5\}$
Answer & Solution
Correct answer: A. $\{x:x<2$ or $x>5\}$
1. The complement holds every real number that $B$ leaves out.
2. $B$ runs from 2 to 5 with both endpoints included.
3. So the complement is everything strictly below 2, together with everything strictly above 5.
4. That is $\{x:x<2\text{ or }x>5\}$.
5. The endpoints must be excluded from the complement precisely because $B$ includes them.
_Source: NECTA ACSEE 2022 Advanced Mathematics 142/1, Question 5: Sets_
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