Question

Se A={x∈R∕x>5/8},B={x∈R∕x<2/3} e C= {x∈R∕5/8≤x≤3/4}, então (AUC)∩B é:

Answer 1

Explicação passo-a-passo:

• $\sf A=\left\{x\in\mathbb{R}~|~x > \dfrac{5}{8}\right\}$

• $\sf B=\left\{x\in\mathbb{R}~|~x < \dfrac{2}{3}\right\}$

• $\sf C=\left\{x\in\mathbb{R}~|~\dfrac{5}{8} \le x \le \dfrac{3}{4}\right\}$

Temos que:

• $\sf A\cup C=\left\{x\in\mathbb{R}~|~\dfrac{5}{8} \le x \le \dfrac{3}{4}~ou~x > \dfrac{3}{4}\right\}$

Logo:

$\sf \red{(A\cup C)\cap B=\left\{x\in\mathbb{R}~|~\dfrac{5}{8} \le x < \dfrac{2}{3}\right\}}$