Question

5.
Fie A = {x EZ | |x| = -x şi | x + 3 | <5}, B = { x EZ | |x| = x şi-5 <2x-1 <5}.
Aflaţi card A+ card B.

Answer 1

Răspuns:

11

Explicație pas cu pas:

$|x| \geqslant 0 \implies - x \geqslant 0 \iff x \leqslant 0$

$|x + 3| < 5 \\ - 5 < x + 3 < 5 \: \: \: | (- 3) \\ \implies - 8 < x < 3$

A = {-7; -6; -5; -4; -3; -2; -1; 0}

=> card(A) = 8

$|x| \geqslant 0 \implies x \geqslant 0$

$-5 < 2x - 1 < 5 \: \: \: | (+ 1) \\ - 4 < 2x < 6 \: \: \: |(: 2) \\ \implies - 2 < x < 3$

B = {0; 1; 2}

=> card(B) = 3

atunci:

$card(A) + card(B) = 8 + 3 = \bf 11$