# Let the relation R be defined on the set A={1,2,3,4,5}by R={$(a,b):\mid a^2-b^2 \mid <\;8.Then\;R\;is\;given\;by$______________.

Toolbox:
• R is set of ordered pair satisfying
• $(a,b) : |a^2-b^2| < 8 \qquad a,b \in \{1,2,3,4,5\}$
$R: \{(a,b):|a^2-b^2| < 8\}$

$|a^2-b^2| < 8$

Let a=1 b=1

we see that $|a^2-b^2|=|1-1|=0 < 8$

$(1,1) \in R$

$a=1 \qquad b=2 => |1^2-2^2|=|-1|=1 < 8$

$a=2 \qquad b=1 => |2^2-1^2|=|3| < 8$

$a=1 \qquad b=2 => |1^2-2^2|=|-3| < 8$

consider $a=5;b=5 \qquad =>|5^2-5^2| =|0|=0 < 8$

$a=6\; b=5 \qquad |6^2-5^2|=|11|=11 < 8$

Therefore set $R=\{(1,1),(1,2),(2,1),(2,2)........(5,5)\}$