Question Number 203351 by Mingma last updated on 17/Jan/24
Answered by witcher3 last updated on 17/Jan/24
$$\mathrm{x}\in\mathrm{E}\cap\mathrm{F}\Leftrightarrow\left(\mathrm{x}\in\mathrm{E}\:\&\mathrm{x}\in\mathrm{F}\right) \\ $$$$\Leftrightarrow\left(\mathrm{x}\in\mathbb{N}\:\&\mathrm{1}\leqslant\mathrm{x}\leqslant\mathrm{15\&}\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\in\mathbb{Z}\right) \\ $$$$\mathrm{x}\in\mathbb{N}\Rightarrow\mathrm{x}\geqslant\mathrm{0}\:\Rightarrow\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\in\mathbb{Z}\Rightarrow\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\geqslant\mathrm{1} \\ $$$$\Leftrightarrow\left\{\mathrm{x}\in\mathbb{N};\mathrm{1}\leqslant\mathrm{x}\leqslant\mathrm{15},\:\mathrm{x}+\mathrm{1}\mid\mathrm{2}\right\},\mathrm{x}=\left\{\mathrm{1},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{9},\mathrm{11},\mathrm{13},\mathrm{15}\right\} \\ $$
Commented by Mingma last updated on 17/Jan/24
Perfect ��