The relation R defined on the set A = 1, 2, 3, 4, 5 by R=(a, b): |a^2…

We have,

$(a, b) ∈R⇔|a^2-b^2|<16$

$∴a=1⇒|1-b^2|<16⇒|b^2-1|<16⇒-15 <b^2 <17$

$⇒ 0<b^2 <17⇒ b=1, 2, 3, 4$

$a=2⇒|4-b^2|<16⇒ |b^2-4|<16⇒-12 <b^2 <20$

$⇒ 0<b^2 <20⇒ b=1, 2, 3, 4$

$a=3⇒|9-b^2|<16⇒|b^2-9|<16⇒-7 <b^2 <25$

$⇒0<b^2 <25⇒ b = 1, 2, 3, 4$

$a=4⇒|16-b^2|<16⇒|b^2-16|<16⇒-0 <b^2 <23$

$⇒b=1, 2, 3, 4, 5$

$a =5⇒ |25 − b^2| <16⇒|b^2 - 25|<16⇒ 9<b^2 <41$

$⇒b=4,5$.

Then,

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