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  • The total number of positive integers not exceeding 1000 that are divisible by 7 or 11 is

The total number of positive integers not exceeding 1000 that are divisible by 7 or 11 is

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Solution:   Let A and B denotes the sets of positive integers not

                   Exceeding 1000 that are divisible by 7 and 11 respectively .

                  Now ,    n(A)=[frac10007]=142;n(B)=[frac100011]=90

                 Rightarrow            n(Acap B)=[frac10007 imes 11]=12.

                 herefore             n(Acup B)=n(A)+n(B)-n(Acap B)=142+90-12=220.

Posted by

Deependra Verma

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