Answer :
Let A = set of students who applied for group I
B = set of students who applied for group II
U = set of students who passed X standard exam
A Λ B = set of students who applied for both groups
A υ B = set of students who applied for group I or group II
~ (A υ B) = set of students who did not apply for any group
U = (A υ B) + ~(A υ B)
Cardinatlity of U = cardinality of ~(A υ B) + cardinality of (A υ B)
150 = 20 + cardinality (A υ B)
A υ B = 150-20 = 130
A υ B = A + B - A Λ B
Cardinality of (A υ B) = cardinality of A + cardinality of B - cardinality of (A Λ B)
130 = 95 + 82 - cardinality ( A Λ B)
Cardinality of A Λ B = 47
So 47 students applied for both groups.
B = set of students who applied for group II
U = set of students who passed X standard exam
A Λ B = set of students who applied for both groups
A υ B = set of students who applied for group I or group II
~ (A υ B) = set of students who did not apply for any group
U = (A υ B) + ~(A υ B)
Cardinatlity of U = cardinality of ~(A υ B) + cardinality of (A υ B)
150 = 20 + cardinality (A υ B)
A υ B = 150-20 = 130
A υ B = A + B - A Λ B
Cardinality of (A υ B) = cardinality of A + cardinality of B - cardinality of (A Λ B)
130 = 95 + 82 - cardinality ( A Λ B)
Cardinality of A Λ B = 47
So 47 students applied for both groups.
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