Let U={10,11,12,13,14,15,16,17},A={10,12,14,16},B={11,12,15,16}U=\left\lbrace10,11,12,13,14,15,16,17\right\rbrace,A={\left\lbrace10,12,14,16\right\rbrace},B=\left\lbrace11,12,15,16\right\rbrace. Find:A′∩B=A^{\prime}\cap B=

A′∩B={11,15}$$A^{\prime}$$\cap B=\left\lbrace11,15\right\rbrace

Let U = { 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 } , A = { 10 , 12 , 14 , 16 } , B = { 11 , 12 , 15 , 16 } U=\left\lbrace10,11,12,13,14,15,16,17\right\rbrace,A={\left\lbrace10,12,14,16\right\rbrace},B=\left\lbrace11,12,15,16\right\rbrace . Find: A ′ ∩ B = A^{\prime}\cap B=

Welcome back. For this problem, we've been given our universal set U, as well as sets A and B, and we'd like to find a complement intersect B. Now, we can do this just by using the sets in roster notation, or we can do this with our Venn diagram. I'll be going through both methods here, and you can choose which one you prefer. This time, I'll be starting by using the Venn diagram, and to use the Venn diagram, we have to begin by filling it in. So please pause the video here and take a second to fill it in. Awesome. Now that we have it filled in. Let's figure out which region or regions represent a complement intersect B. We'll start by locating a complement, and we'll be shading that in yellow. Now, a complement is everything that's inside of our universal set, but not in A. So that's going to be everything that's inside of the box, but not in our circle for set A. So I'm gonna shade in everything here, and you'll notice that we have things that are just in the box, but not in either circle, and we have things that are in our circle for B, but just not in our circle for A. Once we have that shaded in, we want to locate B next, and we'll be shading that in blue. Anything that's shaded with both yellow and blue will turn green, and that will be the stuff in our intersection. Now, B is just represented by the circle for B, so we'll shade in everything in our circle for B. And we can see that the area that got shaded in twice is the area in our circle for B, but not also in the circle for A. So, this region here, this region here is representing our set. A complements intersect B. So the elements in a complement intersect B are just going to be those elements, which we can see are 11 and 15. Now, if we wanted to find this without using the Venn diagram, we would start by finding the elements in a complement, which again, would be all of the elements that are in our universal set, but not also in A. To find a compliments, we would just go through. Our universal set and only take the elements that aren't also in A. For example, we won't be taking 10 because it is an A, but we would be taking 11 because it's not an A. We won't be taking 12 as that's an A, but we would be taking 13, which isn't an A. 14 is an A, so it's not going to be an a compliment, but 15 is not an A, so it will be an a compliment. 16 is an A, so it's not going to be in a compliment, but 17 is not an A, so it will be in a compliment. Once we have a complement, we just need to go through a complement and check to see which of its elements are also in B, as those elements will be in. A complements intersect B. Now we can see that 11 is in both of our sets, so 11 will be in the intersection, but 13 is only in a complement, so it won't be in the intersection. We can see that 15 is in both a complement and B, so it's going to be inside of our intersection, but 17 is only in a complement, so it's not going to be in the intersection. And again, we end up getting that the intersection includes the elements 11 and 15. Great work.

Let U={10,11,12,13,14,15,16,17},A={10,12,14,16},B={11,12,15,16}U=\left\lbrace10,11,12,13,14,15,16,17\right\rbrace,A={\left\lbrace10,12,14,16\right\rbrace},B=\left\lbrace11,12,15,16\right\rbrace. Find:A′∩B=$$A^{\prime}$$\cap B=

A′∩B={11,15}$$A^{\prime}$$\cap B=\left\lbrace11,15\right\rbrace

A′∩B={12,16}$$A^{\prime}$$\cap B=\left\lbrace12,16\right\rbrace

A′∩B={13,17}$$A^{\prime}$$\cap B=\left\lbrace13,17\right\rbrace

A′∩B={10,14}$$A^{\prime}$$\cap B=\left\lbrace10,14\right\rbrace

2. Sets

Intersections and Unions

Quantitative Reasoning

2. Sets

Intersections and Unions

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Multiple Choice

Let $U = {10, 11, 12, 13, 14, 15, 16, 17}, A = {10, 12, 14, 16}, B = {11, 12, 15, 16}$ . Find:
$A^{'} \cap B =$

$Venn diagram showing sets A and B within universal set U, highlighting the intersection and elements outside A but in B.$

$A^{'} \cap B = {11, 15}$

$Venn diagram with sets A and B inside universal set U, showing elements and their intersections.$

$A^{'} \cap B = {12, 16}$

$Venn diagram showing sets A and B within universal set U, with elements labeled and overlapping values 12 and 16.$

$A^{'} \cap B = {13, 17}$

$Venn diagram showing universal set U with subsets A (green) and B (blue), highlighting elements 12 and 16 in their intersection.$

$A^{'} \cap B = {10, 14}$

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Struggling with Quantitative Reasoning?

Let U={10,11,12,13,14,15,16,17},A={10,12,14,16},B={11,12,15,16}U=\(\left\[\lbrace\)10,11,12,13,14,15,16,17\(\right\]\rbrace\),A={\(\left\[\lbrace\)10,12,14,16\(\right\]\rbrace\)},B=\(\left\[\lbrace\)11,12,15,16\(\right\]\rbrace\). Find:A′∩B=A^{\(\prime\)}\(\cap\) B=

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Let $U = {10, 11, 12, 13, 14, 15, 16, 17}, A = {10, 12, 14, 16}, B = {11, 12, 15, 16}$ . Find:
$A^{'} \cap B =$