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

Mathematical Logics - Essay Example It does not only promote proper reasoning but it also enhances a proper use of common sense. The sum of numbers available for Andy are Belle’s; 3+4+7=14 or Carol’s 4+6+8=18 or the sum on my cards=?Let the sum of Andy’s cards be A, Sum of Belles cards is B and some of Carol's 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 Carol's cards and Belle’s cards are not equal(B ≠  C).This means that the sum of my cards is either equal to Carol’s or Belle.This reasoning is derived from the fact 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 possessing these subsets. Secondly, it means that the odd numbers Belle sees are 1, 5 and 9.It is obvious that 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 have another card to add to this which means the sum of my cards can never be 14.That is M>14.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 doubt that I have a 4, a 9 and a five. These answers have arrived after a rigorous process of extensive logical reasoning and application of a little bit of Boolean algebra. The fact 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 actual cards available to Andy are two sets.