A) \[x=39\]
B) \[x=63\]
C) \[39\le x\le 63\]
D) None of these
Correct Answer: C
Solution :
| Let C represents the set of Americans like cheese and A represents the set of Americans like apples. |
| \[C\cap A\] represents the set of Americans like both cheese and apples. |
| \[\therefore \,\,n(C)=63,\] \[n(A)=76,\]and \[n(C\cap A)=x\] |
| We know that, |
| \[n(C\cup A)=n(C)+n(A)-n(C\cap A)\] |
| \[100=63+76-x\] |
| \[\Rightarrow \,x=139-100=39\] and \[n(C\cap A)\le n(C)\] |
| \[\Rightarrow \,x\le 63\] |
| \[\therefore \,\,\,39\le x\le 63.\] |
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