Question

Let W be the set of whole nos. and N the set of natural nos. , a belongs to N such that
aW={ ax : x belongs to W}

1. Describe the set 3W intersection 7W
2. Describe the set 5W intersection 15W

Answer 1

$$\begin{gathered} \mathrm{aW}=\left\{\mathrm{ax}:\mathrm{x}\mathrm{belongs}\mathrm{to}\mathrm{W}\right\} \\ \left(1\right)3\mathrm{W}\mathrm{consists}\mathrm{of}0\mathrm{and}\mathrm{multiples}\mathrm{of}3. \\ 7\mathrm{W}\mathrm{consists}\mathrm{of}0\mathrm{and}\mathrm{multiples}\mathrm{of}7. \\ \mathrm{so},3\mathrm{W}\cap 7\mathrm{W}=\left\{0\right\} \\ \left(2\right)5\mathrm{W}\mathrm{consists}\mathrm{of}0\mathrm{and}\mathrm{multiples}\mathrm{of}5. \\ 15\mathrm{W}\mathrm{consists}\mathrm{of}0\mathrm{and}\mathrm{multiples}\mathrm{of}15. \\ \mathrm{so},5\mathrm{W}\cap 15\mathrm{W}=\left\{0,\mathrm{multiples}\mathrm{of}15\right\}. \end{gathered}$$