Set Theory/Examples/Unions and Intersections 1

Example in Set Theory

Let:

$\ds V_1$

$=$

$\ds \set {v_1, v_3, v_4}$

$\ds V_2$

$=$

$\ds \set {v_2, v_5}$

$\ds V_3$

$=$

$\ds \set {v_1, v_3}$

Then:

$\ds V_1 \cup V_2$

$=$

$\ds \set {v_1, v_2, v_3, v_4, v_5}$

$\ds V_1 \cup V_3$

$=$

$\ds \set {v_1, v_3, v_4}$

$\ds V_2 \cup V_3$

$=$

$\ds \set {v_1, v_2, v_3, v_5}$

$\ds V_1 \cap V_2$

$=$

$\ds \O$

$\ds V_1 \cap V_3$

$=$

$\ds \set {v_1, v_3}$

$\ds V_2 \cap V_3$

$=$

$\ds \O$

Thus:

$V_1$ and $V_2$ are disjoint

$V_2$ and $V_3$ are disjoint.

1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.1$: Sets and Subsets: Problem Set $\text{A}.1$: $4$