Question

Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : |a² – b²| < 8. Then R is given by: ?
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Answer 1

Answer:

Step-by-step explanation:

We have,

`(a,b) in R iff |a^(2)-b^(2)|lt16`

`therefore a=1implies|1-b^(2)|lt16implies|b^(2)-1|lt16implies-15ltb^(2)lt17`

`implies0ltb^(2)lt17impliesb=1,2,3,4`

`a=2implies|4-b^(2)|lt16implies|b^(2)-4|lt16implies-12ltb^(2)lt20`

`implies0ltb^(2)lt20impliesb=1,2,3,4`

`a=3implies|9-b^(2)|lt16implies|b^(2)-9|lt16implies-7ltb^(2)lt25`

`implies0ltb^(2)lt25impliesb=1,2,3,4`

`a=4implies|16-b^(2)|lt16implies|b^(2)-16|lt16implies-0ltb^(2)lt23`

`impliesb=1, 2, 3, 4, 5`

`a=5 implies |25-b^(2)|lt16implies|b^(2)-25|lt16=9ltb^(2)lt41impliesb=4,5`.

Then,

`R={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4),(4,5),(5,4),(5,5)}` Clearly, option (d) is correct.