Chapter 2.6, Problem 1E

(a)

To determine

The value of $\left[8\right]+\left[7\right]$ in ${\mathbb{Z}}_{12}$.

(b)

To determine

The value of $\left[10\right]+\left[9\right]$ in ${\mathbb{Z}}_{12}$.

(c)

To determine

The value of $\left[8\right]\left[11\right]$ in ${\mathbb{Z}}_{12}$.

(d)

To determine

The value of $\left[6\right]\left[9\right]$ in ${\mathbb{Z}}_{12}$.

(e)

To determine

The value of $\left[6\right]\left(\left[9\right]+\left[7\right]\right)$ in ${\mathbb{Z}}_{12}$.

(f)

To determine

The value of $\left[5\right]\left(\left[8\right]+\left[11\right]\right)$ in ${\mathbb{Z}}_{12}$.

(g)

To determine

The value of $\left[6\right]\left[9\right]+\left[6\right]\left[7\right]$ in ${\mathbb{Z}}_{12}$.

(h)

To determine

The value of $\left[5\right]\left[8\right]+\left[5\right]\left[11\right]$ in ${\mathbb{Z}}_{12}$.

(i)

To determine

The value of $3\left[7\right]+4\left[9\right]$ in ${\mathbb{Z}}_{12}$.

(j)

To determine

The value of $8\left[5\right]-2\left[10\right]$ in ${\mathbb{Z}}_{12}$.

(k)

To determine

The value of ${\left[2\right]}^9$ in ${\mathbb{Z}}_{12}$.

(l)

To determine

The value of ${\left[3\right]}^4$ in ${\mathbb{Z}}_{12}$.

(m)

To determine

The value of ${\left[4\right]}^2-{\left[3\right]}^2{\left[6\right]}^3$ in ${\mathbb{Z}}_{12}$.

(n)

To determine

The value of ${\left[2\right]}^3{\left[9\right]}^2+2\left[4\right]$ in ${\mathbb{Z}}_{12}$.

(o)

To determine

The value of $8\left[2\right]-7\left[4\right]\left[3\right]$ in ${\mathbb{Z}}_{12}$.

(p)

To determine

The computations $6{\left[3\right]}^3-4{\left[2\right]}^5$ in ${\mathbb{Z}}_{12}$.