Set Relation Diagrams

How to draw diagrams of Set Relations

Arrow Diagram

Let $A=\{1,2,3\}$ and $B=\{1,3,5\}$. Define relations $S$ and $T$ from $A$ to $B$ as follows: $\forall (x,y)\in A\times B$, $(x,y)\in S\iff x<y$ $T=\{(2,1),(2,5)\}$

Set Relations 2024-10-03 17.49.49.excalidraw

⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠ You can decompress Drawing data with the command palette: ‘Decompress current Excalidraw file’. For more info check in plugin settings under ‘Saving’

Excalidraw Data

Text Elements

1

2

3

1

3

5

S

1

2

3

1

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5

T

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Directed Graph

Only for relations on a set. Let $A=\{3,4,5,6\}$, and define $R$ on $A$ as: $\forall x,y\in A,xRy\iff 2|(x-y)$

Set Relations 2024-10-03 20.23.45.excalidraw

⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠ You can decompress Drawing data with the command palette: ‘Decompress current Excalidraw file’. For more info check in plugin settings under ‘Saving’

Excalidraw Data

Text Elements

3

4

6

5

Link to original