Disjoint Sets/Examples/3 Arbitrarily Chosen Sets

Example of Disjoint Sets

Let:

 $\displaystyle U$ $=$ $\displaystyle \set {u_1, u_2, u_3}$ $\displaystyle V$ $=$ $\displaystyle \set {u_1, u_3}$ $\displaystyle W$ $=$ $\displaystyle \set {u_2, u_4}$

Then:

 $\displaystyle U \cup V$ $=$ $\displaystyle \set {u_1, u_2, u_3}$ $\displaystyle U \cap V$ $=$ $\displaystyle \set {u_1, u_3}$ $\displaystyle V \cup W$ $=$ $\displaystyle \set {u_1, u_2, u_3, u_4}$ $\displaystyle U \cap W$ $=$ $\displaystyle \set {u_2}$ $\displaystyle V \cap W$ $=$ $\displaystyle \O$

Thus $V$ and $W$ are disjoint.