A) \[x=39\]
B) \[x=63\]
C) \[39\le x\le 63\]
D) Nona of the above
Correct Answer: C
Solution :
| [c] Let A denotes the set of Americans who like cheese and B denotes the set of Americans who like apples. Let population of Americans be 100. Then, \[n\,(A)=63,\]\[n\,(B)=76\] Now, \[n\,(A\cup B)=n\,(A)+n\,(B)-n\,(A\,\cap B)\] \[=63+76-n\,(A\,\cap B)\] \[\therefore \] \[n\,(A\cup B)+n\,(A\cap B)=139\] \[\Rightarrow \] \[n\,(A\cap B)=139-n\,(A\cup B)\] But \[n\,(A\cup B)\le 100\] \[\Rightarrow \]\[139-n\,(A\cup B)\ge 139-100=39\] \[\therefore \] \[-\,n\,(A\cup B)\ge 39\] i.e. \[39\le n\,(A\cap B)\] ...(i) Again, \[A\cap B\subseteq A,\]\[A\cap B\subseteq B\] \[\therefore \] \[n\,(A\cap B)\le n\,(A)=63\] And \[n\,(A\cap B)\le n\,(B)=76\] \[\therefore \] \[n\,(A\cap B)\le 63\] (ii) Then, \[39\le n\,(A\cap B)\le 63\] \[\Rightarrow \] \[39\le x\le 63\] |
You need to login to perform this action.
You will be redirected in
3 sec
