- If 2+2=3, then (2+2=3 or unicorns exist).
- If 2+2=3 or unicorns exist then unicorns exist. (since
*not*2+2 = 3) - If 2+2=3 then unicorns exist. (by chaining 1 and 2)

- If 2+2=3, then (2+2=3 or unicorns exist).
[since generally, if P then (P or Q) ; Or to paraphrase, if the first of two claims is true, then at least one of the two claims is true.]

- If 2+2=3 or unicorns exist then unicorns exist.
[since

*not*2+2 =3, and generally, if not P, then if P or Q then Q ; Or again, if the first of two claims is false, but at least one of the two claims is true, then the second one is true.] - If 2+2=3 then unicorns exist. (by chaining 1 and 2)
[And so generally, if the first of two claims is false, then the second one, whatever it is, would follow by this form of argument from the erroneous assumption that the first one was true.]