Given A={2,4,6,8}A=\left\lbrace2,4,6,8\right\rbrace, B={4,8,12,16}B=\left\lbrace4,8,12,16\right\rbrace, C={8}C=\left\lbrace8\right\rbrace, find the following:(A) A∩CA\cap C

{ 8 } \left\lbrace8\right\rbrace

Given A = { 2 , 4 , 6 , 8 } A=\left\lbrace2,4,6,8\right\rbrace , B = { 4 , 8 , 12 , 16 } B=\left\lbrace4,8,12,16\right\rbrace , C = { 8 } C=\left\lbrace8\right\rbrace , find the following: (A) A ∩ C A\cap C

this problem we are given set A which is two, four, six, and eight. We have set B which is four, eight, twelve, and sixteen. Then we have set C which is just eight. And we're asked to find the following. Now part A of this problem asks us to find A and C and we're wanting to find the intersection. Notice that's this upside down U symbol which tells us we're finding an intersection. Now an intersection means that we're looking at everything that is in both A and C. That's what we're looking for. So if I have set a right about here, and I also have set c, these are gonna be the two sets that I have. Now what I'm looking for is I can see in set a we have two, four, and six. And then in set c, I see that we have eight. We also have eight in set a. The only thing we have in common between these sets is eight. So what that means is that the intersection of a and c is going to be eight, and that is the answer to this problem. So this is how you can solve situations where you have intersections, and let's move on to the rest of this example. Hope you found this helpful.

Given A = { 2 , 4 , 6 , 8 } A=\left\lbrace2,4,6,8\right\rbrace , B = { 4 , 8 , 12 , 16 } B=\left\lbrace4,8,12,16\right\rbrace , C = { 8 } C=\left\lbrace8\right\rbrace , find the following: (A) A ∩ C A\cap C

{ 8 } \left\lbrace8\right\rbrace

{ 2 , 4 , 6 } \left\lbrace2,4,6\right\rbrace

{ 2 , 4 , 6 , 8 } \left\lbrace2,4,6,8\right\rbrace

9. Inequalities and Absolute Value

Set Operations and Compound Inequalities

Beginning & Intermediate Algebra

9. Inequalities and Absolute Value

Set Operations and Compound Inequalities

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Multiple Choice

Given $A = {2, 4, 6, 8}$ , $B = {4, 8, 12, 16}$ , $C = {8}$ , find the following:
(A) $A \cap C$

$the set 2 comma 4 comma 6$

$the set 8$

$the set 2 comma 4 comma 6 comma 8$

$ϕ$

Verified step by step guidance

Identify the sets given: $A = \left\lbrace 2, 4, 6, 8 \right\rbrace$, $B = \left\lbrace 4, 8, 12, 16 \right\rbrace$, and $C = \left\lbrace 8 \right\rbrace$.

Recall that the intersection of two sets, for example $A \cap C$, consists of all elements that are common to both sets $A$ and $C$.

List the elements of set $A$ and set $C$ side by side to compare: $A = \{2, 4, 6, 8\}$ and $C = \{8\}$.

Determine which elements appear in both $A$ and $C$. Since \$8$ is the only element in $C$ and it is also in $A$, it is the common element.

Write the intersection set as $A \cap C = \left\lbrace 8 \right\rbrace$, which contains all elements common to both sets.

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