Thus, A and E are _contraries_; I and O are _sub-contraries_; A and I, and also E and O are _subalterns_; A and O, and also E and I are _contradictories_. The following will give a symbolic table of each of the four Judgments or Propositions with the logical symbols attached: (A) "All A is B." (E) "No A is B." (I) "Some A is B." (O) "Some A is not B." The following are the rules governing and expressing the relations above indicated: I. Of the Contradictories: _One must be true, and the other must be false_. As for instance, (A) "All A is B;" and (O) "Some A is not B;" cannot both be true at the same time. Neither can (E) "No A is B;" and (I) "Some A is B;" both be true at the same time. They are _contradictory_ by nature,--and if one is true, the other must be false; if one is false, the other must be true. II. Of the Contraries: _If one is true the other must be false; but, both may be false_. As for instance, (A) "All A is B;" and (E) "No A is B;" cannot both be true at the same time. If one is true the other _must_ be false. _But_, both may be _false_, as we may see when we find we may state that (I) "_Some_ A is B." So while these two propositions are _contrary_, they are not _contradictory_. While, if one of them is _true_ the other must be false, it does not follow that if one is _false_ the other must be _true_, for both _may be false_, leaving the truth to be found in a third proposition. III. Of the Subcontraries: _If one is false the other must be true; but both may be true_. As for instance, (I) "Some A is B;" and (O) "Some A is not B;" may both be true, for they do not contradict each other. But one or the other must be true--they can not both be false. IV. Of the Subalterns: _If the Universal (A or E) be true the Particular (I or O) must be true_. As for instance, if (A) "All A is B" is true, then (I) "Some A is B" must also be true; also, if (E) "No A is B" is true, then "Some A is not B" must also be true. The Universal carries the particular within its truth and meaning. But; _If the Universal is false, the particular may be true or it may be false_. As for instance (A) "All A is B" may be false, and yet (I) "Some A is B" may be either true or false, without being determined by the (A) proposition. And, likewise, (E) "No A is B" may be false without determining the truth or falsity of (O) "Some A is not B." But: _If the Particular be false, the Universal also must be false_. As for instance, if (I) "Some A is B" is false, then it must follow that (A) "All A is B" must also be false; or if (O) "Some A is not B" is false, then (E) "No A is B" must also be false. But: _The Particular may be true, without rendering the Universal true_. As for instance: (I) "_Some_ A is B" may be true without making true (A) "_All_ A is B;" or (O) "Some A is not B" may be true without making true (E) "No A is B."