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\lbrace0,1,2,\ldots,9\right\rbrace},P={\left\lbrace2,4,6,8\right\rbrace},Q={\left\lbrace3,6,9\right\rbrace}. Then find & shade P∩QP∩Q.

P∩Q={6}P\cap Q=\left\lbrace6\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\lbrace0,1,2,\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 .

Welcome back. For this problem, we'd like to label the Venn diagram with the elements that belong in each set, using U, the universal set, as well as P and Q. Then we'd like to find and shade P intersect Q. Now, let's start by labeling the Venn diagram. It's going to be helpful to have every single one of the elements in the universal set listed out, so that we can go through each one, crossing off as we go, and put each one in the right region of the Venn diagram. As you can see, in our universal set, we do have ellipses here, so we probably want to start by rewriting that set so that we can actually see all of the elements. We have a 012, and so on and so forth up to 9. So this is all of the natural numbers from 0 to 9. So let's take a second to list those out. We have that U is the set containing 012345678, and 9. Now that we have all of our elements listed out, let's go through each one and figure out where it belongs on the Venn diagram. We're gonna be checking for each element to see if it is in P, in Q, and in both, and that will determine where it goes by helping us to see which circles the element needs to be in. So first we have 0, and 0 is not in P or in Q. So 0 is going to go in our box for the universal set, but not in either circle. So we can put 0 here, and then that's all set. 1 is also not in P or in Q. So again, it will go in the box, but not in either circle. So let's put it here. Now 2 is inside of P, but it's not inside of Q. So we need to put it in the P circle, but not in the Q circle, so we can put it right here. It's in P, but it's not in Q. Next we have 3, which is in Q but not in P. So here we want to put it in our Q circle, but not also in the P circle. So it's gonna be in this region here. Next we have 4, which is in P but not in Q. So 4 is going to go in our circle for P, but not in our circle for Q. We see that 5 is not in P or in Q, so 5 is going to go in our box, but not in either circle. Next we have 6, which is in both P and Q. So it's going to go in this overlapping region here, so that it's in our circle for P and it's also in our circle for Q. Next we have 7, which is not in either P or Q. So again, it will go in the box, but outside of the circles. 8 is inside of P, but not in queue, so we have to put it in our circle for P but not in queue. And 9 is in Q, but not in P. So it goes in a circle for Q, but not in P. Now that we've gone through all of our elements, we have the Venn diagram labeled. So at this point, all we need to do is find and shade P intersect Q. Now, as a reminder, this is going to be all of the elements that are both in P and in Q. So it has to be the region where the two circles overlap or intersect, because we need any element in both sets to be in both circles. And we know that that's going to be this middle overlapping region here that we're highlighting in yellow. The overlap represents the intersection, so this is P intersect Q. Now to find the elements in this set, we just list the elements in this region in the Venn diagram, and we can see that the only element here is 6, so the only element in P intersect Q is 6. 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\lbrace0,1,2,\ldots,9\right\rbrace},P={\left\lbrace2,4,6,8\right\rbrace},Q={\left\lbrace3,6,9\right\rbrace}. Then find & shade P∩QP∩Q.

P∩Q={6}P\cap Q=\left\lbrace6\right\rbrace

P∩Q={0,1,5,7}P\cap Q=\left\lbrace0,1,5,7\right\rbrace

2. Sets

Intersections and Unions

Liberal Arts Math

2. Sets

Intersections and Unions

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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 $P \cap Q$ .
$Venn diagram with sets U={0-9}, P={2,4,6,8}, Q={3,6,9}, showing intersection P∩Q shaded at element 6.$

$Venn diagram with sets P and Q labeled with elements from 0 to 9, highlighting the intersection containing 6.$

$P \cap Q = {6}$

$Venn diagram with sets P={2,4,6,8} and Q={3,6,9} labeled, shading the intersection containing 6.$

$P \cap Q = {6}$

$Venn diagram with sets P and Q labeled with elements from 0 to 9, highlighting the intersection containing 6.$

$P \cap Q = {0, 1, 5, 7}$

$Venn diagram with sets P={2,4,6,8} and Q={3,6,9} labeled, shading the intersection containing 6.$

$P \cap Q = {0, 1, 5, 7}$

5:28m

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Struggling with Liberal Arts Math?

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∩QP∩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 $P \cap Q$ .
$Venn diagram with sets U={0-9}, P={2,4,6,8}, Q={3,6,9}, showing intersection P∩Q shaded at element 6.$