Question

in survey of425 students in a school it wad found that 115 drink apple juice ,160 drink orange juice and 80 dink both apple as well as orange juice how many drink neither apple nor orange juice

Answer 1

Let the students who drink apple juice be A
therefore,n(A)=115
Let the students who drink orange juice be B
therefore,n(B)=160
80 students drink both
therefore n(A intersection B)=80
n(AUB)=n(A)+n(B)-n(A intersection B)
=115+160-80
=275-80
=195
Therefore,
students who drink neither apple juice nor orange juice=Total no. of students-n(AUB)
=425-195
=230

Answer 2

Step-by-step explanation:

let a denote apple juice and b denote orange juice and u denote total no. of students.

total no of students n(u) = 425

no.of students drinks apple juice n(a) = 115

no of students drinks orange juice n(o) = 160

no of students drinks both apple as well as orange n(a intersection b) = 80

then we have to find n(a' intersection b')

n(a' intersection b') = n ( aUb)'

= n(u) - n( a U b)

= n(u)-n(a)-n(b)+n(a intsec b)

=425-115-160+80

= 230