# Syllogisms

• With Venn diagrams, that show in which intersections of the three sets objects do not (black), can (white) or do (red) exist.
• With Euler diagrams, which are like Venn diagrams with empty regions removed. (Only small diagrams on top of the table.)
• The gist of this page is the reduction of this first-order logic topic to zeroth-order logic using binary square matrices that are essentially 8-ary logical connectives. There are 8 intersections of the three sets, and each intersection can either contain elements or not. So there are 28 = 256 situations that can be the case. Each statement (premise or conclusion) can be denoted by the set of situations in which it is true.

## Graphical elements Venn diagram and corresponding cubic Hasse diagram, used in the diagram on the right The 256 situations that can be the case (minterms)Light vertices indicate that an area is empty, dark vertices indicate that there is at least one element.

## Examples

### Celarent (EAE-1)

Similar: Cesare (EAE-2)

### Darii (AII-1)

Similar: Datisi (AII-3)

### Ferio (EIO-1)

Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4)

### Celaront (EAO-1)

Similar: Cesaro (EAO-2)

### Camestros (AEO-2)

Similar: Calemos (AEO-4)

### Felapton (EAO-3)

Similar: Fesapo (EAO-4)