One about set notation

Question

Which one of the following sets is $(-\infty, b) \cup (c,\infty)$ ?

a)all Real numbers, not including $(c,b)$ if $c <b$

b) all Real numbers, not including $(b,c)$ if $b<c$

c) all Real numbers, not including $[c,b]$ if $c<b$

d) all Real numbers, not including $[b,c]$ if $b<c$

So, at the exam I chose b as the correct answer, but reviewing the exam I noticed that it may well be d, and I actually think that it is in fact d, the right answer, as in the union $b$ and $c$ would not be included, so all real numbers, not including $[b,c]$ the brackets indicate including..does that makes sense? what do you guys think?

Answer 1

I would say the answer is $d$. Since you want to include the numbers $b$ and $c$. For instance, if you took $b=-1$ and $c=1$. Then your set becomes $(-\infty, -1)\cup(1, \infty)$. Therefore the set of numbers you are looking for is all real numbers except for those between and $\mathbf{including}$ $-1$ and $1$. Since they are included as something you don't want. There should be brackets around them, giving the set of all real numbers except $[-1,1]$. Also, clearly in this example $b<c$. Hope this helps!