In a survey of 31 instructors, it was found that 23 liked whiteboards, 16 liked blackboards, and 10 liked both. How many instructors like whiteboards only? How many instructors liked blackboards only? How many instructors liked neither? 

a) 13

b) 6

c) 2

Step-by-step explanation

Total instructors = 31

Instructors who like white boards = 23

Instructors who like black boards = 16

Instructors who liked both = 10

a) Instructors who like whiteboards only = Instructors who like white boards - Instructors who liked both

= 23 - 10

= 13

b) Instructors who like blackboards only = Instructors who like black boards - Instructors who liked both

= 16 - 10

= 6

c) Instructors who liked neither = Total instructors - (Instructors who like whiteboards only + Instructors who like blackboards only + Instructors who liked both)

= 31 - (13 + 6 + 10)

= 31 - 29

= 2

The venn diagram is shown below