## Hypothetical Propositions

A hypothetical proposition has the form "If p, then q," where p and q once again are the component propositions. However, in this case, they are not called disjuncts. The "if" component is called the antecedent and the "then" component is called the consequent.

Example:

In the statement "If it's a girl, then it isn't a boy," the antecedent is "it's a girl," and the consequent is "it isn't a boy."

In a hypothetical proposition, we are not actually asserting the truth of p or q; we are saying that the truth of p would be sufficient to guarantee the truth of q.

Comprehension Questions
 1. What is the standard form of "p if q?" a) if p, then q b) if q, then p c) if not -p, then not -q d) if not -p, then q e) if p then q and if q then p 2. What is the standard form of "p only if q?" a) if p, then q b) if q, then p c) if not -p, then not -q d) if not -p, then q e) if p then q and if q then p 3. What is the standard form of "p if and only if q?" a) if p, then q b) if q, then p c) if not -p, then not -q d) if not -p, then q e) if p then q and if q then p 4. What is the standard form of "p unless q?" a) if p, then q b) if q, then p c) if not -p, then not -q d) if not -p, then q e) if p then q and if q then p

Nonstandard Forms

Hypothetical Syllogisms