Destructive dilemma is a logical rule of inference that says if P implies Q, R implies S, and ~Q or ~S is true, then ~P or ~R is true as well. It is the negative version of a constructive dilemma. Essentially, the destructive dilemma passes the negative statements of the disjunction through two conditional statements. For example, if the statements
“If I am running, I am happy.”
“If I am sleeping, I am dreaming.”
“I am not happy or I am not dreaming.”
are true, then it must also be true that I am not running or I am not sleeping.