Question

A survey of 85 persons was conducted at TCC, and it was found that 54 persons carried a cell phone, 19 persons carried a tablet computer, and 16 carried both a cell phone and a tablet.How many people carried a cell phone or a tablet?How many people carried neither a cell phone nor a tablet?How many people carried a cell phone only?How many people carried a tablet but not a cell phone?

Answer 1

The universal set is given below as

`\xi=85`

The number of people with cell phone is

`n(C)=54`

The number of persons with tablet is

`n(T)=19`

The number of people who carry both cellphone and tablet

`n(C\cap T)=16`

Step 1:

To figure our the number of students that carry cellphone or tablets will be

`\begin{gathered} =38+16+3 \\ =57\text{ }people \end{gathered}`

Hence,

The number of people that carried cell phone or tablet

`\Rightarrow57people`

Step 2:

How many people carried neither a cell phone nor a tablet?

`\begin{gathered} =85-(38+16+3) \\ =85-57 \\ =28 \end{gathered}`

Hence,

The number of people that carried neither cell phone nor a tablet is

`\Rightarrow28people`

Step 3:

How many people carried a cell phone only?

Hence,

The number of people who carried cell-phone only is

`\Rightarrow38people`

Step 4:

How many people carried a tablet but not a cell phone?

Hence,

The number of people that carried a tablet but not a cell phone is

`\Rightarrow3people`