Relations and Functions

Relations and Functions

Question

In a survey of 600 students, 150 were found to be drinking tea and 225 drinking coffee. 100 were drinking both tea and coffee. Find, how many students were neither drinking tea nor coffee?

Answer

Let,                 Set A = set of student whio drink tea
   rightwards double arrow                     n(A)  = 150                                                                         ....(i)
                        Set B = set of student who drink coffee                                     .....(ii)
   rightwards double arrow                 n(B)  = 225                       
Number of student drinking both tea and coffee
      space space space space space space space space space space space space space space space space space space space space equals space straight n open parentheses straight A intersection straight B close parentheses space equals space 100                                                                 ...(iii)
Using,       "<pre
  
          space space space space 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 150 space plus 225 space minus 100 space equals space 275 
Total number of studenr of = 600
space space space space space space space space space rightwards double arrow space space space space space space space space space straight n left parenthesis straight U right parenthesis space equals space 600
Hence, the number of students who neither drink tea nor coffee.
      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 space straight n left parenthesis straight U right parenthesis space minus straight n left parenthesis straight A union straight B right parenthesis
                             = 600 - 275 = 325

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