Question

1) In a parking garage, there are 17 Ford vehicles and 14 Toyota vehicles. There are 23 SUVs and 9 of them are Toyotas. In the Venn diagram below, do the following:(a) Fill in the labels for the sets and the universe in the appropriate blank spaces.(b) Fill in the correct numerical values in the appropriate blank spaces.

Answer 1

Given the following set of cars

`\begin{gathered} T\Rightarrow T\text{oyota} \\ S\Rightarrow\text{SUV} \\ F\Rightarrow\text{Ford} \end{gathered}`
`\begin{gathered} n(F)=17 \\ n(\text{S }\cap\text{ T)}\Rightarrow9 \\ n(S\cap T^(\prime))=23-9=14 \\ n(S^(\prime)\cap T^{})=14-9=5 \end{gathered}`

The universal set is the sum of all the subsets given above

`\begin{gathered} n(U)=n(F)+n(\text{S }\cap\text{ T)}+n(S\cap T^(\prime))+n(S^(\prime)\cap T^{}) \\ n(U)=17+9+14+5=45_{} \end{gathered}`

The Venn diagram is show below