Chapter 2.3A, Problem 3A

To determine

(a)

To explain:

That the given statement $A\cup \varnothing =A$ is true or false for all sets $\text{A}$ and $\text{B}$.

To determine

(b)

To explain:

That the given statement $A-B=B-A$ is true or false for all sets $\text{A}$ and $\text{B}$.

To determine

(c)

To explain:

That the given statement $\overline{A\cap B}=\overline{A}\cap \overline{B}$ is true or false for all sets $\text{A}$ and $\text{B}$.

To determine

(d)

To explain:

That the given statement $\left(A\cup B\right)-A=B$ is true or false for all sets $\text{A}$ and $\text{B}$.

To determine

(e)

To explain:

That the given statement is true or false for all sets $\text{A}$ and $\text{B}$

$\begin{array}{rll}\left(A-B\right)\cup \left(B-A\right)& =& \left\{2\right\}\cup \left\{4\right\}\\ & =& \left\{2,4\right\}\end{array}$.