Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2...

Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8},
N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. (U ∩ ∅′) ∪ R

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we want to find set B. Union with the universal set, intersection with the empty set complement and indicate if they are dis joint sets. So let's go ahead and look at what the problem is asking for and sort of break down the symbols. So to make it easier to know I'm going to make the universal set have this little line at the bottom so I don't get confused with the union symbol and I'm going to start by breaking down what this inner parentheses is saying. So this is inner parentheses is saying universal set, intersection with the empty set complement. So the empty set is a set that contains no values. So the empty set complement would be the opposite of containing no values, which would mean all values. And another set that contains all values is the universal set. So what this inner parentheses is basically saying is universal set intersection with the universal set. And when we think about the universal intersecting itself, they're going to have all the same values, which means that when the universal set intersects itself, we get the universal set back. I'm just gonna go ahead and write that this simple here means intersection. Just to make it clear and we already determined that when the universal set intersects the empty set compliment, we actually get the universal set back because the universal or the empty set complement is the same as the universal set. So now that I've broken down that inner set of parentheses. I'm going to bring back my be set Union, Union with the universal set. And from here we're looking for the values that are in B. Or in the universal set or both. So basically we want to find a set of elements that encompasses every single value in you and every single value and be and by you, I mean the universal set. So we want to find a set of elements that encompasses every single value in the universal set. Well, the good thing about the universal set is that it already encompasses all the values. But we can go ahead and double check this by making sure that the values that are in B are present in the universal set. So I have 35 and it shows up in my universal set. I have 37. It also shows up 39, 39, 41, 41, 43 43. So from this, we can see that the universal set actually encompasses all the values in b. So we can just write the universal set as our union. So we'll have 34 35 37 38 40, 41, 42, 43, 44, 45, 46, 47, 48 and 49 as our final answer. Because this set of numbers encompasses both set B. And the universal set. And you can see that that aligns with answer choice A. So hopefully this video helped and see you next time.

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. (U ∩ ∅′) ∪ R

Key Concepts

Set Theory

Complement of a Set

Disjoint Sets

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