Let A = {3, 5} and B = {7, 11}. Let R = {(a, b): a A, b B, a-b is odd}. Show that R is an empty relation from into B.

Given, A = {3, 5} and B = {7, 11}


R = {(a, b): a A, b B, a-b is odd}


On putting a = 3 and b = 7:


a – b = 3 – 7 = -4 which is not odd


On putting a = 3 and b = 11:


a – b = 3 – 11 = -8 which is not odd


On putting a = 5 and b = 7:


a – b = 5 – 7 = -2 which is not odd


On putting a = 5 and b = 11:


a – b = 5 – 11 = -6 which is not odd


R = { } = Φ


R is an empty relation from into B


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