Question

Some of the cricket players are tennis players, some tennis players are hockey players, no cricket player is a hockey player. Which of the following diagrams correctly represents the above statements?

A.

B.

C.

D.

Answer 1

Hint: In the above question, it is given that some of the cricket players are tennis players, some tennis players are hockey players, and no cricket player is a hockey player. We have been asked to find the correct Venn diagrams among the given options. To find the correct answer we need to find the intersections of the sets and their mutual exclusiveness or independence.

Complete step-by-step answer:
We have given that,
Some of the cricket players are tennis players, some tennis players are hockey players, no cricket player is a hockey player.
Let denote cricket player by A, tennis player by B and hockey player by C
  \[P\left( A\cap B \right)\ne 0\]
Some of the cricket players are tennis player’s i.e.
 \[P\left( A\cap B \right)\ne 0\]
Some tennis players are hockey player’s i.e.
  \[P\left( B\cap C \right)\ne 0\]
No cricket player is a hockey player i.e.
 \[P\left( A\cap C \right)\ne 0\]
So combining all these possibilities the correct figure is that we will show in the figure (c ).
Therefore,
So the option C is the correct answer.
So, the correct answer is “Option C”.

Note: There are many cases which need to be considered for all the three given items, how they all are related to each other and the Venn diagram will be correct only if their relations are explored and inferred correctly. These types of questions is based on the concepts of sets – their intersection and their mutual exclusiveness or independence.