Chapter 2.2, Problem 1E

List $A=\left\{x\in N|x<7\right\},B=\left\{x\in Z|\left|x-2\right|<4\right\}$ and $C=\left\{x\in R|x^3-4x=0\right\}$:

List the elements in each of these sets.

Find $A\cup C,B\cap C,B\backslash C,A\oplus B,C\times \left(B\cap C\right),\left(A\backslash B\right)\backslash C,A\backslash \left(B\backslash C\right),\text{ and }$

$\left(B\cup \varnothing \right)\cap \{\varnothing \}$.

List the elements in $S=\left\{\left(a,b\right)\in A\times B|a=b+2\right\}$ and in $T=\left\{\left(a,c\right)\in A\times C|a\le c\right\}$.