Question

Decide among the following sets, which are subsets of which:
A = { x:x satisfies $x^2-8x+12=0$ }
B = {2,4,6}
C = {2,4,6,8,.....}
D = {6}

Answer 1

$A:\{x:x$ satisfies $x^2-8x+12=0\}$

$x^2-8x+12=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{8\pm \sqrt{64-4\times 1\times 12}}{2\times 1}$

$x=\frac{8\pm \sqrt{64-48}}{2}$

$=\frac{8\pm \sqrt{16}}{2}$

$x=\frac{8+4}{2},\frac{8-4}{2}$

$x=6,2$

$A=\{2,6\}$

$B=\{2,4,6\}$

$C=\{2,4,6,\mathrm{8...}\}$

$D=\left\{6\right\}$

A,B,D are subset of C.