Question

A sports club found that 100 of its members played at least
one of football, tennis or badminton. Thirty-nine played football, 31
played tennis and 51 played badminton. Of these, 9 played both football
and tennis, 8 played both tennis and badminton and 10 played both
football and badminton. How many played just one sport?

Answer 1

Venn diagram, let x be the number of people playing all 3 sports
working from the inside out ...
playing both football and tennis but not badminton = 9-x
playing both football and badminton but not tennis = 10-x
playing both tennis and badminton but not football = 8-x

playing only football = 39 - (9-x) - (10-x) - x = 20 + x
playing only tennis = 31 -(9-x) - x - (8-x) = 14 + x
playing only badminton = .....

sum of all the parts = 100, this will give you x
find all the 3 "playing only ..." parts, then add them up