Question

Please solve this problem. Question in attached figure.​

Answer 1

$\bf A = \{ x~|~x \in \mathbb{N}; x\leq 3 \}$

$\bf x\leq 3\implies x\in \{0,1,2,3\}\implies \green{\boxed{\bf A = \{0,1,2,3\}}}$

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$\bf B = \{ x~|~x \in \mathbb{N};~ 9\leq x^{2}\leq 36 \}$

$\bf 9\leq x^{2}\leq 36\Rightarrow 3^{2} \leq x^{2}\leq 6^{2}\Rightarrow 3\leq x\leq 6\Rightarrow x\in\{3,4,5,6\}$

$\bf x\in \{3,4,5,6\}\implies \blue{\boxed{\bf B = \{3,4,5,6\}}}$

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$\bf C = \{ x~|~x \in \mathbb{N};~ 3< x\leq 7\}$

$\bf 3$

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$\bf D = \{ x~|~x \in \mathbb{N};~ 8\leq x^{3}\leq 100 \}$

$\bf 8\leq x^{3}\leq 100\Rightarrow 2^{3} \leq x^{3}\leq 4^{3}\Rightarrow 2\leq x\leq 4\Rightarrow x\in\{2,3,4\}$

$\bf x\in \{2,3,4\}\implies \red{\boxed{\bf D = \{2,3,4\}}}$

$==Salmon==$