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? o 327 o 119 o 89 o 346

Explanation:

Step1: Recall the principle of set - union for Venn diagrams

To find the number of people who visited Dublin or London, we use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\) for two - sets \(A\) and \(B\). In the context of the Venn diagram, we sum up the non - overlapping and overlapping parts of the circles representing Dublin and London.

Step2: Identify the relevant regions in the Venn diagram

The number of people who visited only Dublin is \(76\), the number of people who visited Dublin and Paris but not London is \(11\), the number of people who visited all three cities is \(24\), the number of people who visited London and Paris but not Dublin is \(24\), and the number of people who visited only London is \(80\).

Step3: Calculate the number of people who visited Dublin or London

We sum up the values in the regions that are part of the Dublin circle or the London circle: \(76 + 11+24 + 24+80=215\). However, if we assume the values in the Venn - diagram are correct and we calculate as follows:
The number of people in the Dublin circle: \(76+11 + 24=111\). The number of people in the London circle: \(80+24 + 24=128\). The number of people in the intersection of Dublin and London is \(24\). Using the formula \(n(D\cup L)=n(D)+n(L)-n(D\cap L)\), where \(D\) represents the set of people who visited Dublin and \(L\) represents the set of people who visited London. So \(n(D\cup L)=(76 + 11+24)+(80 + 24+24)-24=76+11+24+80+24=215\).

Answer:

215