Traditional Square of Opposition

Click for the modern square.

Contradictory pairs of sentences have the opposite truth values. One is true and the other is false.

Contrary pairs of sentences cannot both be true. If one is true then the other is false, but both can be false.

Subcontrary pairs of sentences cannot both be false. If one is false then the other is true, but both can be true.

Subaltern pairs have a more complicated relationship:

If the universal is true, then so is the particular of the same quality. This is the relationship of the A to the I and the E to the O.

If the particular is false, then so is the universal of the same quality. This is the relationship of the I to the A and the O to the E.