Relations and Functions

Relations and Functions

Question

There are 200 individuals with skin disorder. 120 of them are exposed to chemical C1,50 to chemical C2 and 30 to both C1 and C2. Find the number of individuals :

(i) exposed to chemical C1, but not to chemical C2.

(ii) exposed to chemical C2 but not to chemical C1

(iii) exposed to C, or chemical C2 or both.

(iv) not exposed to any of the chemicals C1 and C2.

Answer

Set A = set of individuals exposed to chemical C
space space space space rightwards double arrow space space space space    n(A) = 120                                                                                                           ....(i)
Set B = set individuals exposed to chemical C     
rightwards double arrow n(B) = 50                                                                                                                      .... (ii)
 
Also,                        n (U) = 200                                                                                          ....(iii)

space space space space space space space space space space space space space space space space space space space space space space space space straight n space left parenthesis straight A intersection space straight B right parenthesis space space equals space 30
Using,     space space space space space space space space space space space space space space space space space space straight n left parenthesis straight A union straight B right parenthesis space equals space straight n left parenthesis straight A right parenthesis plus straight n left parenthesis straight B right parenthesis minus straight n left parenthesis straight A intersection straight B right parenthesis,  we get 
                 space space space space space space space space space space space space space space space straight n left parenthesis straight A union straight B right parenthesis space equals space 120 plus 50 minus 30 space equals space 140

∴   (i) Number of individuals exposed to Cbut not to C2. 

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 (ii) Number of individuals exposed to Cbut not to C1. 
space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight n left parenthesis straight B minus straight A right parenthesis space equals space straight n left parenthesis straight b right parenthesis minus straight n left parenthesis straight A intersection straight B right parenthesis space equals space 50 minus 30 equals 20
 (iii) Number of individuals exposed to Cor C2.
space space space space space space space space space space space space space equals space space straight n left parenthesis straight A union straight B right parenthesis space equals space 140
 (i) Number of individuals exposed to Cnor C2.
 
space space space space space space space space space space space space space space space space space space space space space space space space space space equals space straight n space left parenthesis straight A apostrophe intersection straight B apostrophe right parenthesis space equals space straight n left square bracket left parenthesis straight A union straight B right parenthesis apostrophe right square bracket space equals straight n left parenthesis straight U right parenthesis minus straight n left parenthesis straight A union straight B right parenthesis
                           
  = 200 -140 = 60 
 

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