First slide

Introduction to Relations (XI) on Sets

Question

The relation $R$ defined on the set $A = 1, 2, 3, 4, 5$ by $R = (x, y) : | x^{2} - y^{2} | < 16$ is given by

Moderate

A

$R_{1} = (1, 1), (2, 1), (3, 1), (4, 1), (2, 3)$
B

$R_{2} = (2, 2), (3, 2), (4, 2), (2, 4)$
C

$R_{3} = {(3, 3), (4, 3), (5, 4), (3, 4)$
D

none of these

Solution

$(1, 2) \in R$ but $(1, 2) \notin R_{1}$ or $R_{2}$ or $R_{3}$ so $R \neq R_{1}$ or $R_{2}$ or $R_{3}$ .

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