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If $A = {1, 2, 3, 4, 5}$ and $R = {(2, 1), (3, 3), (4, 5), (5, 7)}$ then the set builder form of the relation $' R'$ is

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R = {(x, y) / (x, y) \in A \times A, y = 2 x}

R = {(x, y) / (x, y) \in A \times A, y = 2 x - 3}

R = {(x, y) / (x, y) \in A \times A, y = 2 x + 1}

None

answer is B.

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Detailed Solution

y = 2 x - 3

$x = 1 \Rightarrow y = 2 (1) - 3 = - 1 \notin A$

$x = 2 \Rightarrow y = 1 \in A$

$x = 3 \Rightarrow y = 3 \in A$

$x = 4 \Rightarrow y = 5 \in A$

$x = 5 \Rightarrow y = 7 \in A$

$∴ R = {(2, 1), (3, 3), (4, 5), (5, 7)}$

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