Question

5 Aflați mulțimile A = {x e N*|2x + 4 >_12} și B = {y € N | 2³ < 3^y < 2⁷}.​

Answer 1

Răspuns:

$\bf A = \big\{x\in \mathbb{N^{\star}}~\big|~2x + 4 \geq 12\big \}$

$\bf 2x + 4 \geq 12~~~~ \bigg| -4$

$\bf 2x \geq 12 -4$

$\bf 2x \geq 8~~~\bigg|:2$

$\left.\begin{aligned} \bf x \geq 4\\\\ \bf x\in \mathbb{N^{\star}} \end{aligned}\right\}\implies \purple{\boxed{\bf x \in \big\{1,2,3,4\big\}}}$

$\purple{\boxed{\bf ~A= \big\{1,2,3,4\big\}~}}$

$\bf B = \big\{y\in \mathbb{N}~\big|~2^{3} <3^{y} <2^{7} \big \}$

$\bf ~2^{3} <3^{y} <2^{7}$

$\bf 8 <3^{y} <128\implies 3^{y} \in \big\{9,10,11,...,126,127\big\}$

$\left.\begin{aligned}\bf 3^{y} \in \big\{9,10,...,126,127\big\}~\\\bf3^{2}=9~\\\bf3^{3} =27~\\\bf 3^{4} =84~\\ \bf 3^{5} =243 > 128~\end{aligned}\right\}\Rightarrow\red{\boxed{\bf y \in \big\{2,3,4\big\}}}$

$\red{\boxed{\bf ~B =\big\{2,3,4\big\}~}}$

$==pav38==$