Label the Venn diagram with the elements that belong in each set using U={0,1,2,…,9},P={2,4,6,8},Q={3,6,9}U=\left\lbrace{0,1,2,\ldots,9}\right\rbrace,P={\left\lbrace2,4,6,8\right\rbrace},Q={\left\lbrace3,6,9\right\rbrace}. Then find & shade P∪Q.

P∪Q={2,4,8,6,3,9}P\cup Q=\left\lbrace2,4,8,6,3,9\right\rbrace

Label the Venn diagram with the elements that belong in each set using U = { 0 , 1 , 2 , … , 9 } , P = { 2 , 4 , 6 , 8 } , Q = { 3 , 6 , 9 } U=\left\lbrace{0,1,2,\ldots,9}\right\rbrace,P={\left\lbrace2,4,6,8\right\rbrace},Q={\left\lbrace3,6,9\right\rbrace} . Then find & shade P∪Q.

Welcome back. For this problem, we'd like to label the Venn diagram with the elements that belong in each set. We have our universal set U, and we also have sets P and Q living inside. Then we'd like to find P union Q. All right, so, to fill in our Venn diagram, which is where we need to start, it's going to be helpful to have all of the elements in our universal set listed out. Now, we can see in our universal set that we have some ellipses here. So, I'm gonna start by rewriting the universal set, so I can actually see all of the elements. We can see that in the universal set, we have 012, and so on and so forth to 9. So it looks like here that we have the whole numbers from 0 to 9. That would include 012345678, and 9. So these are all the things that we have to put in our Venn diagram somewhere. Now we're just gonna go through each of our elements of U and see whether those elements are in P, in Q, in both, or in neither. And we'll use that to figure out where to place the element. For example, we noticed the first element of U, 0, is not in P or in Q, so it can't be in either of those circles. So we're gonna put 0 inside of our box, but outside of the circles. Next we have one, which again is not in P or in Q, so we can put it in the box, but outside of the circles. Next we have 2, and we can see that 2 is inside of P, but not inside of Q. So we can put 2 inside of our P circle, but not in that overlapping region that would also be in Q. Next we have 3, and 3 is in Q but not in P. So we can put it in our circle for Q, but outside of our circle for P. Next, we have 4, which is in P but not inside of Q. So 4 will go with 2, inside of our circle for P, but outside of our circle for Q. Next we have 5, which is not in P or Q, so 5 will go in our box for you, but outside of the circles. Next we have 6, and we see that 6 is inside of P and inside of Q. So it will go in this overlapping region here that's inside both P and Q. Next we have 7, and 7 is not in either P or in Q, so we can put 7 inside of our box, but outside of the circles. Then we have 8, and 8 is in P but not in Q, so it will go in our circle for P but not in Q. And finally we have 9, and 9 is just in Q, but not in P, so it will go with 3 in our circle for Q, but not our circle for P. Now that we've gone through all of the elements of the universal set and placed them, we're ready to find P union Q. As a reminder, P union Q is a set of things that are in P, in Q, or in both. So those are going to be the elements inside of the P circle, either not in Q or in this overlapping region as well. And the things in the cue circle, either in that overlapping region or just in our circle for Q. We want to take all of the elements inside of our shaded region here. These are all of the elements inside of at least one of our circles. Now, we're just going to go one region at a time. We can start here on the left, and we see that we have 2. Then 4. Then 8 in the overlap region we have 6. And then just in queue, we have 3 and 9. Now that we've taken each of our elements from inside at least one of our circles, we have all of the elements of P union Q. So we can say that in P union Q, we have 24863, and 9. These elements can be listed in any order, but feel free to reorder them numerically if you'd prefer. Great work.

Label the Venn diagram with the elements that belong in each set using U={0,1,2,…,9},P={2,4,6,8},Q={3,6,9}U=\left\lbrace{0,1,2,\ldots,9}\right\rbrace,P={\left\lbrace2,4,6,8\right\rbrace},Q={\left\lbrace3,6,9\right\rbrace}. Then find & shade P∪Q.

P∪Q={2,4,8,6,3,9}P\cup Q=\left\lbrace2,4,8,6,3,9\right\rbrace

P∪Q={0,1,5,7}P\cup Q=\left\lbrace0,1,5,7\right\rbraceP∪Q={0,1,5,7}

P∪Q={6}P\cup Q=\left\lbrace6\right\rbraceP∪Q={6}

P∪Q={6,3,9}P\cup Q=\left\lbrace6,3,9\right\rbrace

2. Sets

Intersections and Unions

Quantitative Reasoning

2. Sets

Intersections and Unions

Struggling with Quantitative Reasoning?

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Multiple Choice

Label the Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}, P = {2, 4, 6, 8}, Q = {3, 6, 9}$ . Then find & shade P∪Q.

$Venn diagram with sets P={2,4,6,8} and Q={3,6,9} labeled and union P∪Q shaded within universal set U={0–9}.$

$P$\cup$ Q=$\left\[\lbrace$0,1,5,7$\right\]\rbrace$$

$Venn diagram with sets P and Q labeled, elements placed, and the union P∪Q shaded in yellow.$

$P$\cup$ Q=$\left\[\lbrace$6$\right\]\rbrace$$

$Venn diagram with universal set 0-9, sets P={2,4,6,8} and Q={3,6,9}, shaded union of P and Q.$

$P \cup Q = {2, 4, 8, 6, 3, 9}$

$Venn diagram with sets P and Q labeled, elements placed, and union P∪Q shaded in yellow.$

$P \cup Q = {6, 3, 9}$

3:51m

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Struggling with Quantitative Reasoning?

Label the Venn diagram with the elements that belong in each set using U={0,1,2,…,9},P={2,4,6,8},Q={3,6,9}U=\(\left\)\(\lbrace{0,1,2,\ldots,9}\[\right\]\rbrace\),P={\(\left\[\lbrace\)2,4,6,8\(\right\]\rbrace\)},Q={\(\left\[\lbrace\)3,6,9\(\right\]\rbrace\)}. Then find & shade P∪Q.

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Label the Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}, P = {2, 4, 6, 8}, Q = {3, 6, 9}$ . Then find & shade P∪Q.