Question

The relation R defined on a set A = {0,−1, 1, 2} by xRy if |x2 + y2| ≤ 2, then which one of the
following is true?
(1) R = {(0, 0), (0,−1), (0, 1), (−1, 0), (−1, 1), (1, 2), (1, 0)}
(2) R−1 = {(0, 0), (0,−1), (0, 1), (−1, 0), (1, 0)}
(3) Domain of R is {0,−1, 1, 2}
(4) Range of R is {0,−1, 1}

Answer 1

option 2,3,4 are correct.option 1 is wrong as (1,2)does not belong to R as 1^2+2^ 2 is 5 which is not less than 2

Answer 2

(1) is incorrect as (1,2) does not belong to R
(2) is incorrect as it does not include all elements
(4) is also incorrect
so (3) is true