Destructive dilemma

Formally, the destructive dilemma has three premises, it looks as follows:

Premise 1:   A → B   –   (if A, then B)
Premise 2:   C → D   –   (if C, then D)
Premise 3:   ⌐B ∨ ⌐D   –   (not B or not D)
Conclusion:   ⌐A ∨ ⌐C   –   (not A or not C )

Description

The destructive dilemma can be seen as a combination of two Modus Tollens, which are connected by a disjunct statement.

The term “dilemma” in this context should be understood as a “decision” between two conditionals.

Example

An example for a destructive dilemma could be:

If the sun shines tomorrow, [then] we will go to the beach.
If it rains tomorrow, [then] we will go to the museum.
Tomorrow we will either not got to the museum or not go to the beach [or both].
Therefore it will either not rain or the sun will not shine [or both].