Question

the venn diagram shows the number of customers who have purchased different types of pets from a pet store, where c represents customers who have purchased cats, d represents customers who have purchased dogs, and f represents customers who have purchased fish. how many people are in the set c ∩ d? 4 6 36 38

Explanation:

Step1: Recall the definition of intersection

The set \(C\cap D\) represents the customers who have purchased both cats and dogs.

Step2: Identify the relevant region in the Venn - diagram

In a Venn - diagram, the intersection of two sets \(C\) and \(D\) is the region that is common to both circles \(C\) and \(D\). Looking at the Venn - diagram, the number in the region common to \(C\) and \(D\) (excluding the part that is also in \(F\)) is \(3\), and the number in the region common to \(C\), \(D\), and \(F\) is \(1\).

Step3: Calculate \(n(C\cap D)\)

We use the formula for the cardinality of the intersection of two sets in a Venn - diagram (when there is a third - set involved). \(n(C\cap D)=3 + 1\)

Answer:

\(4\)