If $A=\left\{\frac{1}{x}: x \in N\right\}$ and $\left.x<8\right\}$, and $B=\left\{\frac{1}{2 x}: x \in N\right.$ and $\left.x \leq 4\right\}$, find :
(i) $A \cup B$
(ii) $\mathbf{A} \cap \mathbf{B}$
(iii) $A-B$
(vi) $\mathbf{B}-\mathbf{A}$
Given; $A=\left\{\frac{1}{x}: x \in N\right\}$ and $\mathrm{x}<8$ and $B=\left\{\frac{1}{2 x}: x \in N\right\}$ and $\mathrm{x} \leq 4$
According to the given conditions;
$A=\left\{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}\right\}$ and $B=\left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}\right\}$
(i) $A \cup B=$
$\left\{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, \frac{1}{8}\right\}$
(ii) $A \cap B=$
$\left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{6}\right\}$
(iii) $A-B=$
$\left\{1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}\right\}$
(vi) $\mathrm{B}-\mathrm{A}=$
$\left\{\frac{1}{8}\right\}$
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