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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?

yowhatsup123
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    This is not meant to be a challenge. It is only meant to check whether or not you understand the definitions of the symbols as they are presented to you. If you have the boys Adam, Bob, and Charles and I ask to name the boys whose names don't start with the letter B... that should be a simple task that anyone capable of speech can do. This problem is the same with the only differences being that we are talking about numbers and intervals and using symbols instead. Be confident in your ability to answer yourself, not timid. – JMoravitz Mar 15 '22 at 21:19

1 Answers1

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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).

Jack Gallagher
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  • Thank you so much for your answer. I have edited my answer to think what (b) and (c) would be. Could you check if I am thinking in the right direction? – yowhatsup123 Mar 16 '22 at 03:37
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    No worries your answer for part b looks spot on however for part c firstly i would recognise that your set contains 8 so it should be ${2}\cup [4,8]$ which when we take away the elements of B gives us $(6,8]$ if that makes sense :) – Jack Gallagher Mar 16 '22 at 04:12