In the diagram given below, there is a circle, a square and a triangle dividing the region into five disjoint bounded areas. Each of these areas are labelled with number of players belonging to that area. The circle contains cricketers, the square contains football players and the triangle contains hockey players. Region counts: triangle only: 2, triangle and square only: 8, all three: 3, square and circle only: 5, circle only: 8. Which one of the following is not correct?
- AEvery hockey player plays football
- BEvery cricket player plays either football or hockey
- CThere are some hockey players who play both cricket and football
- DThere are some football players who play neither cricket nor hockey
Explanation
Reading the Venn diagram: hockey players (triangle) lie entirely inside the football square, so every hockey player plays football and (A) is correct. The all-three region (3) gives hockey players who also play cricket and football, so (C) is correct, and the square-only region (8) gives football players playing neither of the other games, so (D) is correct. But the circle-only region (8 cricketers) plays neither football nor hockey, so (B) 'every cricket player plays either football or hockey' is the one that is NOT correct.