Question

use the accompanying venn diagram, which shows the cardinality of each region, to answer the question below. how many elements belong to set a or set c? there are elements that belong to set a or set c. (simplify your answer.)

Explanation:

Step1: Recall the formula for \(n(A\cup C)\)

The formula for the number of elements in \(A\cup C\) is \(n(A\cup C)=n(A)+n(C)-n(A\cap C)\). In terms of Venn - diagram regions, elements in \(A\) are the regions \(1,6,7\) and elements in \(C\) are the regions \(1,3,8\). But when we count \(n(A)+n(C)\), the region \(A\cap C\) (the region common to \(A\) and \(C\)) is counted twice.

Step2: Count the regions

Count the regions that belong to \(A\) (regions \(1,6,7\)) and regions that belong to \(C\) (regions \(1,3,8\)).

$$n(A\cup C)=7 + 1+6+3 + 8$$

$$n(A\cup C)=25$$

Answer:

\(25\)