Proof By Contradiction


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Proof By Contradiction is a proofing technique. In this approach, we assume the statement that we are proving to be false. Then, we generate a result that results in contradiction or inconsistency.

Please allow me to use an example to elaborate on it more clearly. Let us assume there are 5 corrugated cartons and 6 FIFA football that needs to be packaged inside and shipped to Qatar World Cup. Well, in case you might be wondering FIFA World Cup is already over, imagine we have time travel ๐Ÿ˜‹. Anyway, it is definitely going to be the case that one carton will have two footballs. It is quite obvious right? Since we only have 5 cartons but 6 footballs.

Now let us make a general statement. Are you ready? ๐Ÿ˜‰

" If there are n cartons and m footballs such that n<m, then there will be at least one carton with more than 1 football. " Now we have a general proposition with us. I am sure you might be wondering what is a proposition.๐Ÿ˜‚ Well a proposition is a statement that is either true or false but not both at the same at the same time.

Moving ahead...

Did you notice what I just did? I observed what happened with 5 cartons and 6 balls and made a general statement. Is this general statement correct? Is it false? Well, how do we know that?

The answer is quite simple...๐Ÿ˜‹

We have multiple proofing techniques available to us. All we need to do is use them accordingly and prove their correctness.

Among them, one is Proof by Contradiction.

Tighten your seat belt folks we will go on a roller coaster ride to understand Proof By Contradiction. It will be a fun journey.

Since you are ready here we go...

We assume the statement is false. By false what we are actually trying to say is no two balls occupy the same carton. Well it can only happen if n>=m . Hence, we were unable to prove it false. Trying to do so created contradiction. Hence, the statement was proven true.

I hope you like my explanation. If you do please offer me a follow ๐Ÿ˜‹... Just kidding!