Create a Venn diagram with the elements that belong in each set using U = { 0 , 1 , 2 , … , 9 } , A = { 1 , 2 , 3 , 4 , 5 } , B = { 2 , 4 , 3 } U={\left\lbrace0,1,2,\ldots,9\right\rbrace},A=\left\lbrace{1,2,3,4,5}\right\rbrace,B=\left\lbrace{2,4,3}\right\rbrace Hint: B⊆A

Welcome back. For this problem, we'd like to create a Venn diagram with the elements that belong in each set. Here, our universal set is the numbers from 0 to 9. A is a set containing 1234, and 5, and B is a set containing 24, and 3. And we are given a hint that says that B is a subset of A. This is something we can check. As a reminder, B is a subset of A if B only contains elements also in A. And we can see that the elements of B, 24, and 3 are also in A, we have here 24, and 3. Now, we have seen a couple examples in our video on subsets, and in a previous example problem of Venn diagrams with subsets. When we have a subset, its circle is going to appear inside of the circle that it's a subset of. So here, we're gonna have a circle in our Venn diagram for set A, which will be blue. Let me draw it in here, circle for set A. And our circle for set B, which will be green, is going to be inside of our circle for set A, because B is a subset of A. Now, this means that anytime we put something in our circle for set B, it is by default also in our circle for set A. So this is a way of representing the fact that everything in B is inside of A. Now that we have all of our regions drawn on the Venn diagram, we just need to put in the elements. Now, I always like to have my universal set written out with every element written so that I can cross it off as I add it, just to make sure that I don't miss anything. So I'm first going to write the elements of my universal set. We have 012345678, and 9. And now we just go through those elements and see which sets those elements are in. We start with 0, which is in the universal set, but not in either A or B. So we need to make sure it's in the box, but not in either of the circles. So I'm just going to put 0 here and cross it off. Next we have 11 is in A, but it's not in B. So I need to make sure it is inside of the circle for A, but not in the circle for B. So let's put it here. Cross it off. Then we have 2, which is inside of A and B. So I need to put 2 inside of my circle for B. As a reminder, because the circle for B is inside of the circle for A, 2, being in the circle for B, means it's also in the circle for A. So we're all set there, and we can cross off 23 is also in both A and B, so we'll put it in the circle for B, which means it's in the circle for A. And we have the same thing happening with 4. It's also in both A and B, so we'll put 4 in our circle for B and cross it off. Next we have 5, which is inside set A, but not in set B, so we need to put it in the circle for A, but not in the circle for B. Next we have 6, which is in the universal set, but it's not in either A or B, so we have to put it in the box, but not in either circle. So let's just put it here. We see the same thing for 7. It's in the universal set, but not in either set A or set B. So we'll just put it in our box. And the same thing is going to happen with 8 and 9. Both 8 and 9 are in the universal set, but not in either set A or set B. So again, they have to go in the box, but not in either circle. So we'll put 8 here maybe, and we'll put 9 over here. Now that we've put in all of the elements of our universal set, we are all set, and we have our Venn diagram ready to go. Great work.

2. Sets

Subsets

Quantitative Reasoning

2. Sets

Subsets

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Multiple Choice

Create a Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}, A = {1, 2, 3, 4, 5}, B = {2, 4, 3}$
Hint: B⊆A

$Venn diagram showing universal set 0-9 with set A containing 1-5 and subset B containing 2, 3, 4 inside A.$

$Venn diagram showing universal set 0-9, set A with 1-5, and subset B with 2, 3, 4 inside A.$

$Venn diagram showing universal set U with sets A and B inside, B fully contained within A, displaying their elements.$

$Venn diagram showing universal set U with numbers 0-9, set A with 1,2,3,4,5, and subset B with 2,3,4 inside A.$

5:20m

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Struggling with Quantitative Reasoning?

Create a Venn diagram with the elements that belong in each set using U={0,1,2,…,9},A={1,2,3,4,5},B={2,4,3}U={\(\left\[\lbrace\)0,1,2,\(\ldots\),9\(\right\]\rbrace\)},A=\(\left\[\lbrace{1,2,3,4,5}\]\right\[\rbrace\),B=\(\left\]\lbrace{2,4,3}\[\right\]\rbrace\)Hint: B⊆A

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Create a Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}, A = {1, 2, 3, 4, 5}, B = {2, 4, 3}$
Hint: B⊆A