GATE Civil 2021 Set 2 | GA Question: 8

Question

1. Some football players play cricket.
2. All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements $1$ and $2$ above, is :

• A. No football player plays hockey
• B. Some football players play hockey
• C. All football players play hockey
• D. All hockey players play football

Answer 1

Given statements are:

1. Some football players play cricket.  

   

2. All cricket players play hockey.

   

• A. No football player plays hockey – It is not correct. No way we can combine diagrams 1 and 2 to get a diagram for this statement. 
• B. Some football players play hockey – It is correct from the above reasoning. In whichever way we combine the Venn diagrams of the given two statements we’ll get an intersection for Football and Hockey.
• C. All football players play hockey – It can be true but not always and the counterexample is shown in the below Venn diagram which can be obtained by combining the Venn diagrams for the given statements.

  

• D. All hockey players play football – It also can be correct but not always. The counterexample shown in the above Venn diagram for option C works here as well.

So, the correct answer is $(B).$