A survey was conducted to know the hobby of 220 students in class 9. out of which 130 students informed about their hobby as rock climbing and 180 students informed about their hobby as sky watching. There are 110 students who followed both the hobbies. then how many students don't have both of the hobbies?, how many students only prefer Rock climbing? , How many students follow only sky watching?

A survey was conducted to know the hobby of 220 students in class 9. o

1.	A survey was conducted to know the hobby of 220 students in class 9. out of which 130 students informed about their hobby as rock climbing and 180 students informed about their hobby as sky watching. There are 110 students who followed both the hobbies. then how many students don't have both of the hobbies?, how many students only prefer Rock climbing? , How many students follow only sky watching?
Answer» Let A be rock climbing hobby =130Let B be the sky WATCHING hobby =180n(A∩B)=110Total STUDENTS (U)=220Hencen(A∪B)=N(A)+n(B)−n(A∩B) =130+180−110 =200Let n(A∪B) ′ = Who do not have EITHER hobbyn(A∪B) ′ =n(U)−n(A∪B) =220−200 =20Therefore 20 students do not have both hobbyStudent's who only like rock climbing =n(A)−n(A∩B) =130−110 =20Students who only like sky watching =n(B)−n(A∩B) =180−110 =70