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

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. (R ∪ N) ∩ M′

Accepted Answer

Hello. Everyone in this video. We're going to be looking at this practice problem where we want to find a union with D. Intersection with the C. Compliment set. And we want to indicate if there's any dis joint sets and were given the universal set. You set a set C. And C. D. So before getting started on this problem I'm going to go ahead and rewrite the set of elements that we're trying to find. So a union with D. Intersection with the C. Compliment. And I'm going to go ahead and write the words out for these symbols. So I don't get confused. So first I have a union with D. And for the union that means I want the values in set A. And seven D. Or both. So I just want to make sure that whenever I write this set out it has all the values in C. And C. D. And the second symbol here is the intersection. So that means I want only the values that are shared between the two sets. And now I can go ahead and get started. So I'm going to work with this set of parentheses. First this a union with D. So if I write a union with d. I need to make sure to write all the values in set a. So that's 34 38 and 42. And those in set D. Which is 34 41 42 or and 45. So from this set you can see that there's some repeats because set a. And set d share values and because they share some values they are not dis joint sets. So I'm going to go ahead and eliminate the values that I've written twice. So you can see that they both have 34. So I've written 34 twice. So I'll go ahead and erase that 2nd 34. They both have 38 which means I've written 38 twice and I'll go ahead and erase that. And those are the two values that they share. So my new set for when I have a union with the D. Is 34 36 38 40 41 44 45. And now I can worry about the second portion where I need to find the C. Compliment. So C compliment means I want to get all the values that are in the universal set and not in set C. Which essentially means I want to eliminate all the values that are in set c. From my universal set. So set c. 44, eliminate that from my universal set. 45 will also eliminate that. 46 47 and 48. So now all the numbers that are left in my universal set that are not crossed off become part of my C. Compliments set. So I have 34 36 37 39 40 42 43 and 49. So now I've solved both sides of this. A union with D. Intersection with C. Compliment. And now I need to worry about the intersection so now I want only the values that are shared between both of these sets that I've just solved for. So from this you can see that both of them have 30 for 36 38 42 not 44 Or 45. So only the ones that I've highlighted in black hair or underlined in black. So if I write them out again I'm writing a union with D. Intersection with the C. Complement. This set of numbers becomes 36 38 Or 40 41 42. That's it. And because both a union with D. And and C. Compliment have shared values. I know that they're not dis joint sets. So this becomes my final answer 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. (R ∪ N) ∩ M′

Key Concepts

Set Operations (Union, Intersection, Complement)

Universal Set and Complement

Disjoint Sets

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