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.

In logical operator notation

where represents the logical assertion.

In sum, this argument states that if one premise implies another, and another implies a third, and either the first premise or the second premise is true, then one of the conclusions is true, or the other is true. 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 or Jimmy Carter wins the election.

Therefore, either Jimmy Carter or Ronald Reagan will be the president.

The Dilemma derives its name because of the transfer of disjunctive operants. Because one cannot have P&R, one cannot have both Q&S. In this example, the situation in which Ronald Reagan and Jimmy Carter are both presidents produces a logical contradiction.