Question

If A = {1, 2, 3} and the relation R = {(x, y); x2 – y2≤5,, ∈}, then write R as a set of ordered pair.

Answer 1

Given :   A = {1, 2, 3}

relation R = {(x, y); x²– y²≤5,, ∈}

To Find :  R as a set of ordered pair.

Solution:

x²– y²≤5

possible value of x are  1 , 2 , 3

1² - 1²  ,1²  - 2²  , 1²  - 3²    ≤5   Hence ( 1 , 1) , (1  ,2 ) , (1 , 2)

2² -  1²  , 2² - 2²  , 2² - 3²    ≤5   Hence ( 2 , 1) , (2  ,2 ) , (2 , 2)

3² - 1² > 5

3² - 2²  = 5   ,  3² - 3² <  5   Hence ( 3 , 2) , ( 3 ,3)

R = { ( 1, 1) , ( 1 ,2 ) , ( 1 , 3) , (2 , 1) , (2 , 2) , (2 , 3) , ( 3 , 2) , ( 3 , 3) }

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