Question

give two example each explain why associative property is not true for subtraction and division

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}\mathrm{are}\mathrm{whole}\mathrm{numbers}. \\ \mathrm{Now},\mathrm{a}+\left(\mathrm{b}+\mathrm{c}\right)=\left(\mathrm{a}+\mathrm{b}\right)+\mathrm{c}\left[\mathrm{For}\mathrm{addition}\right] \\ \mathrm{a}\times \left(\mathrm{b}\times \mathrm{c}\right)=\left(\mathrm{a}\times \mathrm{b}\right)\times \mathrm{c}\left[\mathrm{For}\mathrm{multiplication}\right] \\ \mathrm{Now},\mathrm{assocative}\mathrm{law}\mathrm{hold}\mathrm{true}\mathrm{for}\mathrm{addition}\mathrm{and}\mathrm{multiplication}. \\ \mathrm{Consider}3\mathrm{whole}\mathrm{numbers}1,2\mathrm{and}3. \\ \mathbf{For}\mathbf{}\mathbf{addition}\mathbf{}\mathbf{:} \\ \mathrm{Now},1+\left(2+3\right)=1+5=6 \\ \left(1+2\right)+3=3+3=6 \\ \mathbf{For}\mathbf{}\mathbf{multiplication}\mathbf{}\mathbf{:} \\ 1\times \left(2\times 3\right)=1\times 6=6 \\ \left(1\times 2\right)\times 3=2\times 3=6 \\ \mathrm{Hence},\mathrm{associative}\mathrm{law}\mathrm{holds}\mathrm{true}\mathrm{for}\mathrm{multiplication}\mathrm{and}\mathrm{addition}. \\ \mathrm{Now},\mathrm{it}\mathrm{does}\mathrm{not}\mathrm{hold}\mathrm{true}\mathrm{for}\mathrm{subtraction}\mathrm{and}\mathrm{division}. \\ \mathrm{a}-\left(\mathrm{b}-\mathrm{c}\right)\ne \left(\mathrm{a}-\mathrm{b}\right)-\mathrm{c} \\ \mathrm{a}÷\left(\mathrm{b}÷\mathrm{c}\right)\ne \left(\mathrm{a}÷\mathrm{b}\right)÷\mathrm{c} \\ \mathrm{Consider}3\mathrm{numbers}\mathrm{as},1,2,3. \\ \mathbf{For}\mathbf{}\mathbf{subtraction}\mathbf{}\mathbf{:} \\ 1-\left(2-3\right)=1-\left(-1\right)=1+1=2 \\ \left(1-2\right)-3=-1-3=-4 \\ \mathbf{For}\mathbf{}\mathbf{division}\mathbf{}: \\ 1÷\left(2÷3\right)=1÷\left(\frac{2}{3}\right)=1\times \frac{3}{2}=\frac{3}{2} \\ \left(1÷2\right)÷3=\frac{1}{2}÷3=\frac{1}{2}\times \frac{1}{3}=\frac{1}{6} \\ \mathrm{Hence},\mathrm{associative}\mathrm{law}\mathrm{does}\mathrm{not}\mathrm{hold}\mathrm{true}\mathrm{for}\mathrm{subtraction}\mathrm{and}\mathrm{division}. \end{gathered}$$