Question

Se xe y são dois conjuntos não vazio, então (x-y)u(xny) e igual a

Answer 1

$\displaystyle \sf \text{Podemos representar } : \\\\ x-y = x\cap \overline{y}\\\\Da{\'i}}: \\\\ (x-y)\cup(x\cap y)\\\\ (x\cap\overline{y})\cup(x\cap y) \\\\ \left[(x\cap \overline{y}) \cup x\right] \ \cap\ \left[(x\cap \overline{y}) \cup y \right] \\\\ \left[\underbrace{\sf (x\cup x)}_{x} \ \ \cap \underbrace{\sf (x\cup \overline{y})}_{U \ (universo)}\right] \ \cap\ \left[(x\cup y)\ \cap\ \underbrace{\sf (y\cup \overline{y})}_{U \ (universo)} \right]$

$\displaystyle \sf \left[x\ \cap\ U\right ] \ \cap\ \left[ (x\cup y)\ \cap U\right] \\\\ x \cap (x\cup y) \\\\ (x\cap x) \cup (x\cap y) \\\\ x \cup (x\cap y) = x$
portanto :

$\displaystyle \sf \huge\boxed{\sf\ (x-y)\cup(x\cap y) = x \ }\checkmark$