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Given the following sets, find the set A’ n (B U C ‘)

Given the following sets, find the set A’ n (B U C ‘)-example-1
User Sparanoid
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Answer:


A^(\prime)\cap(B\cup C^(\prime))=\lbrace1,7,8,9,10\rbrace

Explanations:

Given the following sets of numbers:


\begin{gathered} U=\mleft\lbrace1,2,3,\ldots10\mright\rbrace \\ A=\mleft\lbrace2,\text{ 3, 4, 6}\mright\rbrace \\ B=\mleft\lbrace1,\text{ 3, 8}\mright\rbrace \\ C=\mleft\lbrace1,\text{ 3, 4, 5, 8}\mright\rbrace \end{gathered}

Before we get the required set, we will need to get the complement of set A (A') and the complement of set C'.

Compliments of a set are the elements in the universal set but not in the original set.

The complements of A and C are given as:


\begin{gathered} A^(\prime)=\mleft\lbrace1,5,7,8,9,10\mright\rbrace \\ C^(\prime)=\mleft\lbrace2,\text{ 6, 7, }9,\text{ 10}\mright\rbrace \end{gathered}

For the element of the set A' n (B U C')

First, we need to get (BUC')


B\cup C^(\prime)=\mleft\lbrace1,2,3,6,7,8,9,10\mright\rbrace

Note that the union of two sets (U) is the combination of all the elements in both sets without repeating elements.


A^(\prime)\cap(B\cup C^(\prime))=\mleft\lbrace1,7,8,9,10\mright\rbrace

Note that the intersection of two sets (n) are the common elements in both given sets.

User Speedogoo
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