Constructive dilemma

A logical constructive dilemma is a formal logical argument that takes the form:

1a) P → Q.

b) R → S.

2) Either P or R is true.

Therefore, either Q or S is true.

$p \rightarrow q$

$r \rightarrow s$

$p \lor r$

$\therefore q \lor s$ .

In sum, if two conditionals are true and at least one of their antecedents is, then at least one of their consequents must be too.

An example:

If Ronald Reagan wins the election, he will be President.

If Jimmy Carter wins the election, he will be President.

Either Ronald Reagan wins the election or Jimmy Carter wins the election.

Therefore, either Jimmy Carter will be President or Ronald Reagan will be President.

The Dilemma derives its name because of the transfer of disjunctive operants.