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)
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.
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].
- Destructive dilemma on Wikipedia