Question

6. Fie multimile:
A={x € N | x² < 36} B={ x € N | x³ <64}
a) Scrieti elementele multimilor A,B.
b) Calculati A U B, A n B, A — B, B — A.
c) Reprezentati aceste multimi folosind diagrama Venn-Euler ​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

A ={0,1,2,3,4,5}

x^3 < (2^2)^3, deci x < 2^2 = 4, cu x natural

B = {0,1,2,3}

b)

A U B = A

A ∩ B = B

A - B = {4,5}

B - A = Ф(multimea vida)

c)

poza

Answer 2

$\it x\in\mathbb{N},\ \ x^2<36 \Rightarrow x^2<6^2 \Rightarrow x<6 \Rightarrow A=\{0,\ \ 1,\ \ 2,\ \ 3,\ \ 4,\ \ 5\}\\ \\ x\in\mathbb{N},\ \ x^3<64 \Rightarrow x^3<4^3 \Rightarrow x<4 \Rightarrow B=\{0,\ \ 1,\ \ 2,\ \ 3\}\\ \\ A\cup B=\{0,\ \ 1,\ \ 2,\ \ 3,\ \ 4,\ \ 5\};\ \ A\cap B=\{0,\ \ 1,\ \ 2,\ \ 3\}\\ \\ A-B=\{4,\ \ 5\};\ \ \ B-A=\varnothing$