mehul vaidya
u are absolutely correct. Since the question is not giving any information about the people who don't speak any of the languages, we should not neglect it.
| E | = 18, | H | =15 , |K| =22 , |E∩ H| =9 , |E∩K| = 11 , |H∩K|, |E∩H∩K| =X
Let the people who don't speak any of the languages is Y;
According to the principle of Mutual Exclusion:
|E∪ H∪ K| = 18 + 15+ 22 -(9+11+13) + X
28 - Y = 22 + X
X + Y = 6 ----------(1)
There are 7 possible pairs of values which satisfy this equation here;
(6,0),(5,1)(4,2)(3,3)
Since we have to follow the options, we will take pair(6,0) indicates X =6 otherwise X can be 5, 4,3,2,1,0