Operations On Sets

n(A)%3D10%2C%20n(B)%3D15%2C%20n(20)%2C%20n(A%20%5Ccap%20B)%3D8%2C%20n(B%20%5Ccap%20C)%3D9

possible value of

n

(AUBUC)

n(A%20%5Ccup%20B%20%5Ccup%20C)%3Dn(A)%2Bn(B)%2Bn(C)-n(A%20%5Ccap%20B)%20-n(B%20%5Ccap%20C)-n(A%20%5Ccap%20C)%20%2Bn(A%20%5Ccap%20B%20%5Ccap%20C)

%3D10%2B15%2B20-8-9-n(A%20%5Ccap%20C)%2Bn(A%20%5Ccap%20B%20%5Ccap%20C)

%3D28-n(A%20%5Ccap%20C)%2Bn(A%20%5Ccap%20B%20%5Ccap%20C)

We see here,

28-n(A%20%5Ccap%20C)%2Bn(A%20%5Ccap%20B%20%5Ccap%20C)%20%5Cgeqslant%200

%5CRightarrow%20n(A%20%5Ccup%20B%20%5Ccup%20C)%20%5Cleqslant%2028%5C%2C%5C%2C%5C%2C...(1)

We see,

n(A%20%5Ccup%20B)%3Dn(A)%2Bn(B)-n(A%20%5Ccap%20B)

%3D10%2B15-8

%3D17

n(B%20%5Ccup%20C)%20%3Dn(B)%2Bn(C)-n(B%20%5Ccap%20C)

%3D15%2B20-9

%3D26

Obviously,

n(A%20%5Ccup%20B%20%5Ccup%20C)%20%5Cgeqslant%2026

also,

n(A%20%5Ccup%20B%20%5Ccup%20C)%20%5Cgeqslant%2017%5C%2C%5C%2C%5C%2C%20...(2)

%5Ctherefore

from (1) & (2)

26%20%5Cleqslant%20n(A%20%5Ccup%20B%20%5Ccup%20C)%20%5Cleqslant%2028

Chapter Questions
1 MCQs