Chapter DPT, Problem 31E

Each statement illustrates the use of one of the following real number properties or definitions. Indicate which one.

   $\begin{array}{lll}\text{commutative}\left(+,\cdot \right)\hfill & \text{Associative}\left(+,\cdot \right)\hfill & \text{Distributive}\hfill \\ \text{Identity}\left(+,\cdot \right)\hfill & \text{Inverse}\left(+,\cdot \right)\hfill & \text{Subtraction}\hfill \\ \text{Division}\hfill & \text{Negatives}\hfill & \text{Zero}\hfill \end{array}$

(A)     $\left(-7\right)-\left(-5\right)=\left(-7\right)+\left[-\left(-5\right)\right]$

(B)     $5u+\left(3v+2\right)=\left(3v+2\right)+5u$

(C)     $\left(5m-2\right)\left(2m+3\right)=\left(5m-2\right)2m+\left(5m-2\right)3$

(D)     $9\cdot \left(4y\right)=\left(9\cdot 4\right)y$

(E)     $\frac{u}{-\left(v-w\right)}=\frac{u}{w-v}$

(F)     $\left(x-y\right)+0=\left(x-y\right)$