Answer :

Put a = 1 , b = 1 |12 – 12| ≤ 5, (1, 1) is an ordered pair.


Put a = 1 , b = 2 |12 – 22| ≤ 5, (1, 2) is an ordered pair.


Put a = 1 , b = 3 |12 – 32| > 5, (1, 3) is not an ordered pair.


Put a = 2 , b = 1 |22 – 12| ≤ 5, (2, 1) is an ordered pair.


Put a = 2 , b = 2 |22 – 22| ≤ 5, (2, 2) is an ordered pair.


Put a = 2 , b = 3 |22 – 32| ≤ 5, (2, 3) is an ordered pair.


Put a = 3 , b = 1 |32 – 12| > 5, (3, 1) is not an ordered pair.


Put a = 3 , b = 2 |32 – 22| ≤ 5, (3, 2) is an ordered pair.


Put a = 3 , b = 3 |32 – 32| ≤ 5, (3, 3) is an ordered pair.


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


(i) For (a, a) є R


|a2 – a2| = 0 ≤ 5. Thus, it is reflexive.


(ii) Let (a, b) є R


(a, b) є R è |a2 – b2| ≤ 5


|b2 – a2| ≤ 5


(b, a) є R


Hence, it is symmetric


(iii) Put a = 1 , b = 2 , c = 3.


|12 – 22| ≤ 5


|22 – 32| ≤ 5


But |12 – 32| > 5


Thus, it is not transitive.


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