Here there is no direct predication concerning Joe Smith, but only a predication of one of the alternatives conditionally on the other being denied, as, _If Joe Smith was not a prophet he was an impostor_; or, _If he was not an impostor, he was a prophet_.

Symbolically, Disjunctives may be represented thus: A is either B or C, Either A is B or C is D.
Formally, every Conditional may be expressed as a Categorical.

For our last example shows how a Disjunctive may be reduced to two Hypotheticals (of which one is redundant, being the contrapositive of the other; see chap.vii.Sec.

10).

And a Hypothetical is reducible to a Categorical thus: _If the sky is clear, the night is cold_ may be read--_The case of the sky being clear is a case of the night being cold_; and this, though a clumsy plan, is sometimes convenient.