Hypothetical Propositions:
Nonstandard Forms
"p if and only if q"

When we want to claim that the truth of either p or q implies the truth of the other, we combine the preceding forms into: "p if and only if q." As the word "and" suggests, we are making two statements:

"p if q," which becomes, "If q, then p"
AND

"p only if q, which becomes, "If p, then q"

This analysis makes it clear that in the "if and only if" construction, both p and q serve as antecedents, and both also serve as consequents.


"p if q" | "p only if q" | "p if and only if q"
"p unless q" | "Whenever p, q" | "Without p, then q"


Hypothetical Propositions

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