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 { 8 }

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 { 8 }

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

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

2. Linear Equations and Inequalities

Set Operations and Compound Inequalities

Intermediate Algebra

2. Linear Equations and Inequalities

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) $A \cap C$

$\left\lbrace2,4,6\right\rbrace$

$\left\lbrace8\right\rbrace$

$\left\lbrace2,4,6,8\right\rbrace$

$\phi$

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, $A \cap C$, consists of all elements that are common to both sets $A$ and $C$.

Compare the elements of set $A$ with those of set $C$ to find which elements appear in both sets.

List the common elements found in both $A$ and $C$ to form the intersection set $A \cap C$.

Write the intersection set $A \cap C$ using set notation, enclosing the common elements in curly braces.

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