Question

The relation $R$ defined on the set $A=\{1,2,3,4,5\}$ as $R=\left\{\right(a,b):|a^2-b^2|<16\}$ has cardinality equal to

Answer 1

$(a,b)\in R⟺|a^2-b^2|<16$
$a=1\Rightarrow |1-b^2|<16\Rightarrow b=1,2,3,4$
$a=2\Rightarrow |4-b^2|<16\Rightarrow b=1,2,3,4$
$a=3\Rightarrow |9-b^2|<16\Rightarrow b=1,2,3,4$
$a=4\Rightarrow |16-b^2|<16\Rightarrow b=1,2,3,4,5$
$a=5\Rightarrow |25-b^2|<16\Rightarrow b=4,5$
∴ Total number of elements $=19$