Relations and Functions

Relations and Functions

Question

Write the set : space space space space space open curly brackets 1 third comma 2 over 4 comma 3 over 5 comma 4 over 6 comma 5 over 7 comma 6 over 8 comma close curly brackets in the set- builder form.

Answer
space space space space space space space straight A space equals space open curly brackets 1 third comma space 2 over 4 comma space 3 over 5 comma space 4 over 6 comma 5 over 7 comma 6 over 8 close curly brackets space space space space space space space space space space space space rightwards double arrow space space space space space space space space straight x space equals space 1 third comma space 2 over 4 comma space 3 over 5 comma space 4 over 6 comma 5 over 7 comma 6 over 8

Numerator in each element is a natural number less than equal to 6
The denominator in each element is 2 more than the numerator
rightwards double arrow                          space space space space space space space space straight x space equals space fraction numerator straight n over denominator straight n plus 2 end fraction comma space straight n space less or equal than 6


Hence,   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 space space space straight A space equals space left curly bracket space straight x space colon space straight x space equals fraction numerator straight n over denominator straight n plus 2 end fraction comma space straight x space element of space straight N comma space straight n space less or equal than space 6 right curly bracket

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