If [1+1=3] Then ["m" is the first alphabetic letter]
This little mind teaser should be no challenge to anyone in the computer industry or mathmaticians, or generally anyone who has minimal knowledge in logic...
The statement is a Tautology (ie. always true). A formal proof goes like this:
Say, p: 1+1=3 , q: "m" is the first alphabetic letter
p => q
= ~p + q ; since p is a contradiction, so always ~p
= TRUE ; since always ~p
For the ones not familiar with logic operators, here is a friendly demonstration (as simple as I can put it):
Since, ( If X Then Y ) is equivalent to ( Y OR NOT X ) [see below]*
If [1+1=3] Then ["m" is the first alphabetic letter]
= ["m" is the first alphabetic letter] OR NOT [1+1 is Equal to 3]
= ["m" is the first alphabetic letter] OR [1+1 is Not Equal to 3]
= ["m" is the first alphabetic letter] OR TRUE
= TRUE [see below]**
* Consider this statement: If [You Study] Then [You Pass]... This statement holds in three conditions: 1- You Study AND Pass, OR 2- You dont Study AND Fail, OR 3- You dont Study AND Pass.... So from {1,3} the statement holds when you Pass (whether you study or not), OR from {2,3} it holds when you dont study (wether you pass or not)! So the statement is equivalent to: [You Pass] OR [You don't Study]! So ( If X Then Y ) is equivalent to ( Y OR NOT X ) as required!!
** Consider this statement: [Your Pen's Color is Blue] OR [Sunday follows Saturday]... The second part of the statement (ie. Sunday follows Saturday) is always true, so the statement is always true regardless wether the Pen's Color is Blue or not... So, ( [Any Statement] OR [True Statement] ) is necessarily True!!
So, any conclusion based on an always false condition is necessarily true!! So when someone tells you: "If now I had a million dollars, I will unrelectantly give them all to you!!" dare not call him a liar, cuz no matter how cynical this statement might seem - This person is no liar, he is speaking an undeniable truth!!
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