Question

Given the universal set {$x$ : $xϵN$ and x < 20}, then find : B = {y : y = 2n + 3, $nϵN$}.

Answer 1

$U=\{x:x\in N,x<20\}$
$B=\{y:y=2n+3,n\in N\}$
$n=1⟹y=2\left(1\right)+3=5$

$n=2⟹y=2\left(2\right)+3=7$

$n=3⟹y=2\left(3\right)+3=9$

$n=4⟹y=2\left(4\right)+3=11$

$n=5⟹y=2\left(5\right)+3=13$

$n=6⟹y=2\left(6\right)+3=15$

$n=7⟹y=2\left(7\right)+3=17$

$n=8⟹y=2\left(8\right)+3=19$
For $n=9$, we will get $y=21$ but $21\nless 20$$\because$ universal set has values less than 20.

$\therefore B=\{5,7,9,11,13,15,17,19\}$