Relations and Functions

Relations and Functions

Question

In a group of people, 50 speak both English and Hindi and 30 speak English but not Hindi. If all the people speak at least one of the two languages, how many speak English?

Answer

Set A = set of people who speak English
We have to find n(A)
Set B = set of peoplewho speak Hindi.
Number of people who speak English but not Hindi = n(A-B)
         rightwards double arrow  space space space straight n left parenthesis straight A minus straight B right parenthesis space equals space straight n left parenthesis straight A right parenthesis space space minus straight n space left parenthesis straight A intersection straight B right parenthesis
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#6 {main}</pre>                                                                                         ....(i)
Number  of people who speak both English and Hindi
space space space space space space space space space space space equals space straight n left parenthesis straight A intersection straight B right parenthesis space equals space 50                                                                                                        ....(ii)

from (i) and (ii), we have 
n(A) - 50 = 30
rightwards double arrow   n(A)  = 50+30 = 80
Hence, the number of people who speak English
    = n(A) = 80
    

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