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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