Chapter 1.4, Problem 1E

a)

To determine

Whether the set $B$ is closed with respect to the given binary operation defined on the sets of integers $\text{Z}$.

b)

To determine

Whether the set $B$ is closed with respect to the given binary operation defined on the sets of integers $\text{Z}$.

c)

To determine

Whether the set $B$ is closed with respect to the given binary operation defined on the sets of integers $\text{Z}$.

d)

To determine

Whether the set $B$ is closed with respect to the given binary operation defined on the sets of integers $\text{Z}$.

e)

To determine

Whether the set $B$ is closed with respect to the given binary operation defined on the sets of integers $\text{Z}$.

f)

To determine

Whether the set $B$ is closed with respect to the given binary operation defined on the sets of integers $\text{Z}$.

g)

To determine

Whether the set $B$ is closed with respect to the given binary operation defined on the sets of integers $\text{Z}$.

h)

To determine

Whether the set $B$ is closed with respect to the given binary operation defined on the sets of integers $\text{Z}$.