ANPEC 2003 - Q1

por temujin Seg Abr 08, 2013 5:18 pm

A respeito dos conjuntos A,B,C e D definidos abaixo, assinale V ou F:

$\small \inline \\ A=\left \{ x\in\mathbb{R}:|x|<3 \right \} \ \ ; \ \ B=\left \{ x \in \mathbb{R}: x^2+2x<3 \right \} \\ \\ C=\left \{ x \in \mathbb{R}: 1 < e^{lnx}<3 \right \} \ \ ; \ \ D=\left \{ (x,y) \in \mathbb{R}^2: |x|<4, |y|>1 \right \}$

A: -3 < x < 3
B: x²+2x-3 < 0, x'=-3, x''=1, logo: -3 < x < 1
C: 1 < x < 3
D: -4 < x < 4 ; y > 1 e y < -1

(0) $\small \inline A \cup B = B \cup C$

F.

$\small \inline \\ A \cup B = (-3,3) \cup (-3,1)=(-3,3) \\ \\ B \cup C = (-3,1) \cup (1,3)\\ \\ 1 \in (A \cup B), 1 \notin (B \cup C)$

(1) $\small \inline (A \cap B) \cup (A \cap C)=A$

F.

$\small \inline \\(A \cap B) = B = (-3,1) \\ \\ (A \cap C)= C = (1,3)\\ \\ 1 \in A, 1 \notin B, 1 \notin C$

(2) $\small \inline B \cap C = \varnothing$ .

V.

$\small \inline B \cap C = (-3,1)\cap (1,3) = \varnothing$

(3) $\small \inline (B \cup C) \supset A$ .

F.

$\small \inline (B \cup C) \subset A$

(4) $\small \inline B \times C \subset D$ .

V.

$\small \inline B \times C = (-3,1) \times (1,3)$