Answer to Question #273307 in Discrete Mathematics for Jay

Question

A survey of 119 persons was conducted at TTC, and it was found that 89 persons carried a cell phone, 10 person carried a tablet computer, and 8 carried both cellphone and tablet.

1. how many people carried a cellphone or a tablet?
2. how many people carry neither a cell phone nor a tablet? 
3. how many people carried a cell phone only?
4. how many people carried a tablet but not a cell phone?

Answer 1

1.

$$N(C\cup T)=N(C)+N(T)-N(C\cap T)$$

$$=89+10-8=91$$

2.

$$N((C\cup T)')=N(U)-N(C\cup T)$$

$$119-91=28$$

3.

$$N(C-T)=N(C)-N(C\cap T)=89-8=81$$

4.

$$N(T-C)=N(T)-N(T\cap C)=10-8=2$$