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Question: R is a relation from {11, 12, 13} to {8, 10, 12} defined by \(y = x - 3\) . Then \(R ^ { - 1 }\) is...

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y=x−3y = x - 3 . Then R−1R ^ { - 1 } is

A

{(8, 11), (10, 13)}

B

{(11, 18), (13, 10)}

C

{(10, 13), (8, 11)}

D

None of these

Answer

{(8, 11), (10, 13)}

Explanation

Solution

R is a relation from {11, 12, 13}to {8, 10, 12} defined by y=x−3⇒x−y=3y = x - 3 \Rightarrow x - y = 3

∴ R = {11, 8},{13, 10}.

Hence, R−1={8,11};{10,13}R ^ { - 1 } = \{ 8,11 \} ; \{ 10,13 \}.