A and B are two sets such that n (A) = 4 and n(B) = 8. Find the minimum value of n(A  B).

Asked by Topperlearning User | 17th Apr, 2014, 11:58: AM

Expert Answer:

We know that:

I f space A space a n d space B space a r e space f i n i t e space s e t s space a n d space A intersection B space not equal to space 0 comma space t h e n

n open parentheses A union B close parentheses equals n open parentheses A close parentheses space plus space n open parentheses B close parentheses space minus space n open parentheses A intersection B close parentheses

N o w comma space space n open parentheses A intersection B close parentheses space less or equal than space M i n open curly brackets n open parentheses A close parentheses comma space n open parentheses B close parentheses close curly brackets equals M i n open curly brackets 4 comma space 8 close curly brackets equals 4

rightwards double arrow minus n open parentheses A intersection B close parentheses space greater or equal than minus 4

rightwards double arrow n open parentheses A close parentheses plus n open parentheses B close parentheses minus n open parentheses A intersection B close parentheses greater or equal than n open parentheses A close parentheses plus n open parentheses B close parentheses space minus space 4

rightwards double arrow n open parentheses A union B close parentheses greater or equal than 8
H e n c e comma space t h e space m i n i m u m space v a l u e space o f space n left parenthesis A union B right parenthesis space i s space 8.

Answered by  | 17th Apr, 2014, 01:58: PM