I am given the sets A = {2,4,6,8}, B = [2,6)andC = (3,8)`. Calculate each of the following.
(a) B\A
(b) A ∩ B
(c) (A ∪ C)\B
I think the answer for (b) is {2,4} because B is 2 <= x < 6 and A has the elements 2,4,6,8. so in A and B we are going to have {2,4}. Is that the intersection, am I thinking right?
Also, for (c), I think A ∪ C should be {2,8} ∪ [4,8) because my set A contains 2,4,6,8 while C contains 3 < x < 8. But what when I exclude B from this? How should I do that?
It's important here to understand the notation for B and C which are a half open interval and an open interval respectively. This means that in B the number 2 is an element of the interval but 6 is not. If you are unfamiliar with intervals [2,6) is equivalent to $2\leq x <6$ for $x \in \mathbb{R}$.
Using this in (a) we would see that B\A, which is the interval B excluding the elements of A. This could be written as $(2,4)\cup(4,6)$ or if you find it easier to visualise, $(2<x<4)\cup(4<x<6)$. I believe that the rest are homework questions but hopefully this gives a general idea for how to move forward. If you need further help it would be nice for you to explain what you have already tried for parts (b) and (c).