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In a School 150 students passed X Standard examination. 95 students applied for

Group I and 82 students applied for Group II in the Higher Secondary course. If 20 students applied neither of the two, how many students applied for both groups?

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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)