Constructive dilemma

In logic, a constructive dilemma is a formal logical argument that takes the form:


 * 1a) P &rarr; Q.
 *  b) R &rarr; S.


 * 2) Either P or R is true.

Therefore, either Q or S is true.

In logical operator notation
 * $$ P \rightarrow Q $$
 * $$ R \rightarrow S $$
 * $$ P \lor R $$
 * $$ \therefore Q \lor S $$.

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 Ronald Reagan will be President or Jimmy Carter will be President.

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