Question

question
a venn diagram of a and b is given below
find $(a\cap b)^c$.
provide your answer below:

Explanation:

Step1: Find \(A\cap B\)

\(A\cap B\) is the intersection of sets \(A\) and \(B\), which contains elements common to both sets. From the Venn - diagram, \(A\cap B=\{8,3\}\)

Step2: Find \((A\cap B)^c\)

\((A\cap B)^c\) (complement of \(A\cap B\)) is the set of all elements in the universal set (elements in either \(A\) or \(B\)) that are not in \(A\cap B\).
The elements in \(A\) are \(\{14,-6,7,8,3\}\) and the elements in \(B\) are \(\{8,3,2,-5,0\}\). The universal set (elements in \(A\cup B\)) is \(\{14,-6,7,8,3,2,-5,0\}\)
Removing the elements of \(A\cap B\) (i.e., remove \(8\) and \(3\)) from the universal set, we get \((A\cap B)^c=\{14, - 6,7,2,-5,0\}\)

Answer:

\(\{14, - 6,7,2,-5,0\}\)