# The difference between absurd reasoning and contraposal reasoning

What is the difference between absurd reasoning and contraposal reasoning? To show that a language is not regular

• What's the context in which you encountered these terms? Can you tell us more? – D.W. Dec 13 '17 at 6:13
• I saw in different exercises, to shiw that a language is not regular we can use absurd reasoning or contraposal reasoning... – SARR Dec 13 '17 at 17:18
• Ex for L=anbn.... People use absurd or contraposal... I want to know the difference with this two cases. – SARR Dec 13 '17 at 17:19

• RAA in the form of "if $P$ holds then we can derive a contradiction, therefore $\not P$ holds" is fine. That's how you prove a negative statement like "$L$ is not a regular language". This case, however, is almost always conflated with "if $\not P$ holds then we can derive a contradiction, therefore $P$ holds", which is what "proof by contradiction" often refers to and I agree this form of reasoning should be avoided,. This applies to proofs that use $(\neg P\to\neg Q)\to(Q\to P)$ too (but not the converse). Many CS results are amenable to constructive proofs which are clearer. – Derek Elkins Dec 14 '17 at 0:17