Let $U=\{a, b, c, d, e, f, 4,5,6,7,8,9\}, X=\{a, b, c, 5,6,7\}$, and $Y=\{b, d, f, 4,6,8\}$. List the members of the set $X^{\prime} \cap Y^{\prime}$, using set braces.

$X ^{\prime} \cap Y ^{\prime}=\{ \square \}$ (Use a comma to separate answers as needed.)

Question

Let $U=\{a, b, c, d, e, f, 4,5,6,7,8,9\}, X=\{a, b, c, 5,6,7\}$, and $Y=\{b, d, f, 4,6,8\}$. List the members of the set $X^{\prime} \cap Y^{\prime}$, using set braces.

$X ^{\prime} \cap Y ^{\prime}=\{ \square \}$ (Use a comma to separate answers as needed.)

GinnyAnswer · Answer

Find the complement of set X in U : X ′ = { d , e , f , 4 , 8 , 9 } . 
 Find the complement of set Y in U : Y ′ = { a , c , e , 5 , 7 , 9 } . 
 Find the intersection of X ′ and Y ′ : X ′ ∩ Y ′ = { e , 9 } . 
 The members of the set X ′ ∩ Y ′ are { e , 9 } ​ . 
 
 Explanation 
 
 Understanding the Problem We are given the universal set U = { a , b , c , d , e , f , 4 , 5 , 6 , 7 , 8 , 9 } , the set X = { a , b , c , 5 , 6 , 7 } , and the set Y = { b , d , f , 4 , 6 , 8 } . We want to find X ′ ∩ Y ′ , where X ′ is the complement of X in U and Y ′ is the complement of Y in U . 
 
 Finding the Complement of X First, let's find the complement of X in U , which is the set of all elements in U that are not in X . X ′ = U − X = { d , e , f , 4 , 8 , 9 } . 
 
 Finding the Complement of Y Next, let's find the complement of Y in U , which is the set of all elements in U that are not in Y . Y ′ = U − Y = { a , c , e , 5 , 7 , 9 } . 
 
 Finding the Intersection Now, we need to find the intersection of X ′ and Y ′ , which is the set of all elements that are in both X ′ and Y ′ . X ′ ∩ Y ′ = { d , e , f , 4 , 8 , 9 } ∩ { a , c , e , 5 , 7 , 9 } = { e , 9 } . 
 
 Final Answer Therefore, X ′ ∩ Y ′ = { e , 9 } .

Examples 
 Understanding set operations like complements and intersections is crucial in various fields, such as database management and data analysis. For instance, imagine a database of customers. If set X represents customers who purchased product A and set Y represents customers who purchased product B, then X ′ ∩ Y ′ would represent customers who did not purchase product A but also did not purchase product B. This information can be valuable for targeted marketing campaigns or understanding customer preferences.

Anonymous · Answer

The members of the set X ′ ∩ Y ′ are {e, 9}. To find this, we calculated the complements of sets X and Y, then found their intersection. The final result is {e, 9}. 
 ;

Let $U=\{a, b, c, d, e, f, 4,5,6,7,8,9\}, X=\{a, b, c, 5,6,7\}$, and $Y=\{b, d, f, 4,6,8\}$. List the members of the set $X^{\prime} \cap Y^{\prime}$, using set braces. $X ^{\prime} \cap Y ^{\prime}=\{ \square \}$ (Use a comma to separate answers as needed.)

Answer (2)

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Let $U=\{a, b, c, d, e, f, 4,5,6,7,8,9\}, X=\{a, b, c, 5,6,7\}$, and $Y=\{b, d, f, 4,6,8\}$. List the members of the set $X^{\prime} \cap Y^{\prime}$, using set braces.

$X ^{\prime} \cap Y ^{\prime}=\{ \square \}$ (Use a comma to separate answers as needed.)