78
Logically Equivalent Statements
Venn diagrams permit us to identify or remember logically equivalent statements. Such statements have exactly the same truth value (whether true or false) as the original. The Venn diagrams in Figure 18 permit us to identify which apparent equivalences are valid (identical Venn diagrams) and which are invalid (different Venn diagrams).
Valid equivalent statements:
| All S are P: |  |
No S are non-P: | |
| All S are P: | |
All non-P are non-S: | |
| No S are P: |  |
No P are S: | |
| No S are P: | |
All S are non-P: | |
| Some S are P: |  |
Some P are S: | |
| Some S are P: | |
Some S are not non-P: | |
| Some S are not P: |  |
Some S are non-P: | |
| Some S are not P: | |
Some non-P are not non-S: | |
Superficially similar but non-equivalent statements:
| All S are P: | |
No P are non-S: | Missing Figure |
| All S are P: | |
All P are S: | Missing Figure |
| Some S are not P: S | |
Some P are not S: | Missing Figure |
Figure 18. Valid and invalid equivalent statements, and their Venn diagrams.
