In a survey of 350 random people ​, 230 had at least one tattoo, 210 had at least one piercing​, and 175 had both tattoos and piercings.

Question

how many only had tattoos

how many only had piercings 

how many did not have piercings or tattoos

 

Answer 1

Let:

• S = the number of people surveyed
• T= the set of people with tattoos
• P = the set of people with piercings.

 

Draw a Venn diagram with two overlapping sets T and P.  The following information is given:

• n(S) = number of people surveyed = 350
• n(T) = number of people with tattoos = 230
• n(P) = number of people with piercings = 210
• n(T∩P) = number of people with both tattoos and piercings = 175

 

How many had only tattoos?  n(T only) = n(T) - n(T∩P) = 230 - 175 = 55

 

How many had only piercings? n(P only) = n(P) - n(T∩P) = _____

 

How many had neither? n(neither) = n(S) - [ n(T) + n(P) - n(T∩P) ] = _____