Practicing Success
The relation R defined on the set $A = \{1, 2, 3, 4, 5\}$ by $R=\{(a, b): |a^2-b^2|<16\}$ is given by |
$\{(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)\}$ $\{(2, 2), (3, 2), (4, 2), (2, 4)\}$ $\{(3, 3), (4, 3), (5, 4), (3, 4)\}$ none of these |
none of these |
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, |