orange juice. Example There are individuals with a skin disorder, had been exposed to the chemical C , to chemical C , and to both the chemicals C and C . Find the number of individuals exposed to Chemical C but not chemical C (ii) Chemical C but not chemical C (iii) Chemical C or chemical C Solution Let U denote the universal set consisting of individuals suffering from the skin disorder, A denote the set of individuals exposed to the chemical C and B denote the set of individuals exposed to the chemical C . Here n ( U) = , n ( A ) = , n ( B ) = and n ( A ∩ B ) = (i) From the Venn diagram given in Fig .
, we have A = ( A – B ) ∪ ( A ∩ B ). n (A) = n ( A – B ) + n ( A ∩ B ) (Since A – B) and A ∩ B are disjoint.) or n ( A – B ) = n ( A ) – n ( A ∩ B ) = – = Hence, the number of individuals exposed to chemical C but not to chemical C is . (ii) From the Fig . , we have B = ( B – A) ∪ ( A ∩ B).
and so, n (B) = n (B – A) + n ( A ∩ B) (Since B – A and A ∩ B are disjoint.) or n ( B – A ) = n ( B ) – n ( A ∩ B ) = – = Fig . MATHEMATICS Thus, the number of individuals exposed to chemical C and not to chemical C is . (iii) The number of individuals exposed either to chemical C or to chemical C , i.e., n ( A ∪ B ) = n ( A