Mathematical Logics Essay Example | Topics and Well Written Essays - 500 words

Mathematical Logics - Essay ExampleIt does not only promote straight-laced reasoning but it also enhances a proper use of common sense.The tot up of numbers uncommitted for Andy are Belles 3+4+7=14 or Carols 4+6+8=18 or the sum on my peckers=?Let the sum of Andys cards be A, Sum of Belles cards is B and some of Carols cards be C and the sum of my cards is M. So M=B or M=C. This is because we are told that there are at least two card sums which are equal. The sum of Carols cards and Belles cards are not equal(B C).This means that the sum of my cards is either equal to Carols or Belle.This reasoning is derived from the point that Andy admitted that there are two people with an equal sum of cards.The union of odd numbers is 1,3,5,7 and 9.Also, Belle admits that he can see all the five odd numbers, what does this imply? Firstly Belle cannot see 3 and 7 since he is the one takeing these subsets. Secondly, it means that the odd numbers Belle sees are 1, 5 and 9.It is unmistakable t hat Andy possesses the card with 1 on it. Who has 9 and 5? Since there is no one else in the game, it is obvious that I possess cards with 9 and 5.From above, the sum of my cards so far is 9+5=14.I still commit another card to add to this which means the sum of my cards can never be 14.That is M14.Therefore it is obvious that the sum of my cards is 18 since it is the only remaining (M=18).14+X=M=18.X=18-14=4.This means my third card is 4.Therefore my cards are 9, 5 and 4.In conclusion from the above calculations and reasoning, it is evident beyond reasonable interrogative sentence that I have a 4, a 9 and a five. These answers have arrived after a besotted process of extensive logical reasoning and application of a little bit of Boolean algebra. The event that there were three sets of cards visible to Andy, that is mine, Carol and Belle enable me to come down to the situation that the literal cards available to Andy are two sets.