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"

"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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