(b) If the particular is true, the corresponding universal may, or, may not, be true.
If I is true, as “Some men are wise,” or, “Some men are mortal,” then A may be false, as “All men are wise,” or, A may be true, as “All men are mortal.” Or, if O is true, as “Some men are not wise,” or, “Some men are notimmortal,” then E may be false, as “No men are wise”; or, true, as “No men are immortal.”
Second Relation.
(2) If the universal is false, the particular under it may or may not be true, but, if the particular is false, the universal above it must be false.
Illustrations.
(a) If the universal is false, the particular under it may or may not be true.
If A is false, as “All metals are compounds,” or “All men are wise,” then I may be false, as “Some metals are compounds,” or, I may be true, as “Some men are wise.” Or, if E is false, as “No men are mortal,” or, “No men are wise,” then O may be false, as “Some men are not mortal,” or, O may be true, as “Some men are not wise.”
(b) If the particular is false, the universal above it must be false.
If I is false, as “Some men are trees,” then A is false, as “All men are trees.” Or, if O is false, as “Some men are not bipeds,” then E is also false, as “No men are bipeds.”
4. Contradictory Propositions.