Question

the venn diagram below shows survey results of cities visited by a group of people in recent trip to europe. how many people visited dublin or london? 349 68 119 327

Explanation:

Step1: Recall the principle of inclusion - exclusion for Venn diagrams

For two - set Venn diagrams (in this case, Dublin and London), the number of elements in \(A\cup B\) is \(n(A)+n(B)-n(A\cap B)\). Here, the number of people who visited Dublin \(n(D)=76 + 40+24 + 11=151\), the number of people who visited London \(n(L)=80+24 + 40+35 = 179\), and the number of people who visited both \(n(D\cap L)=24 + 40=64\).

Step2: Calculate \(n(D\cup L)\)

Using the formula \(n(D\cup L)=n(D)+n(L)-n(D\cap L)\), we substitute the values: \(n(D\cup L)=151 + 179-64\). First, \(151+179 = 330\), then \(330-64=266\).

Answer:

266