in a survey taken at a mall 71 respondents said they owned a car and 58 of those respondents said they owned a bicycle as well there were eight respondents who said they owned a bicycle only and of those there were three who said they owed neither vehicle

This is what's known as a Venn Diagram relationship. The people who have cars make up one circle. The people who have bicycles make up another circle. The people who have both are in the area where the two circles overlap. The people who have neither a car nor a bicycle are outside both circles.

From that we can set up equations.

Let C = number of people who own a car only

So then,

C + 58 = 71 because they tell us that 71 people said they own a car and 58 of them also a bicycle

C = 71 - 58 = 13 people who ONLY own a car.

The number of people who own bicycles is 58 + 8 = 64 because 58 own a car AND a bicycle and 8 only own a bicycle

So then we now know,

13 people only own a car 64 people own bicycles and 3 people don't own either.