As we have admitted the possibility of joining as alternatives terms which are not really different, the question arises, How shall we treat two or more alternatives when they are clearly shown to be the same? If we have it asserted that P is Q or R, and it is afterwards proved that Q is but another name for R, the result is that P is either R or R. How shall we interpret such a statement? What would be the meaning, for instance, of “wreath or anadem” if, on referring to a dictionary, we found *anadem* described as a wreath? I take it to be self-evident that the meaning would then become simply “wreath.” Accordingly we may affirm the general law A ꖌ A = A. Any number of identical alternatives may always be reduced to, and are logically equivalent to, any one of those alternatives. This is a law which distinguishes mathematical terms from logical terms, because it obviously does not apply to the former. I propose to call it the *Law of Unity*, because it must really be involved in any definition of a mathematical unit. This law is closely analogous to the Law of Simplicity, AA = A; and the nature of the connection is worthy of attention. Few or no logicians except De Morgan have adequately noticed the close relation between combined and disjunctive terms, namely, that every disjunctive term is the negative of a corresponding combined term, and *vice versâ*. Consider the term Malleable dense metal. How shall we describe the class of things which are not malleable-dense-metals? Whatever is included under that term must have all the qualities of malleability, denseness, and metallicity. Wherever any one or more of the qualities is wanting, the combined term will not apply. Hence the negative of the whole term is Not-malleable or not-dense or not-metallic. In the above the conjunction *or* must clearly be interpreted as unexclusive; for there may readily be objects which are both not-malleable, and not-dense, and perhaps not-metallic at the same time. If in fact we were required to use *or* in a strictly exclusive manner, it would be requisite to specify seven distinct alternatives in order to describe the negative of a combination of three terms. The negatives of four or five terms would consist of fifteen or thirty-one alternatives. This consideration alone is sufficient to prove that the meaning of *or* cannot be always exclusive in common language. Expressed symbolically, we may say that the negative of ABC is not-A or not-B or not-C; that is, *a* ꖌ *b* ꖌ *c*. Reciprocally the negative of P ꖌ Q ꖌ R is *pqr*. Every disjunctive term, then, is the negative of a combined term, and *vice versâ*. Apply this result to the combined term AAA, and its negative is *a* ꖌ *a* ꖌ *a*.