Logical Reasoning Math Problem Example | Topics and Well Written Essays - 1250 words

analytical Reasoning - Math Problem ExampleEuler circles otherwise known as Euler diagrams are graphical representations of pellucid statements. Each set in this diagram is represented as a circle or unappealing curve. Intersections between sets are shown as parti completelyy overlapping circles. On the other hand, the equivalence of two sets is precondition by a complete overlap of the circles. utilise this approach, the family relationship of sets becomes clear. It is then easy to determine the rigourousness of a conclusion based on the diagram.For the first statement it is clear from the diagram that given the premise, in that respect is no established relation between B and C. Likewise, the atomic number 42 statement also establishes no relationship between the two. Therefore, twain statements are invalid.In contrast, truth tables are textual representations of the logic statement. Unlike a pure logic statement, the truth table presents all possible combinations of the input set and determines the conclusion from each(prenominal) combination. While not as intuitive as Euler circles, this approach provides a more exhaustive popular opinion of a logical statement. The respective truth tables for the above logical statements followIn the first table, when all the premises are satisfied, there is definitely no way wherein the conclusion is satisfied. This statement is therefore invalid. For the second statement, most cases satisfy the statement except for one. However, since the conclusion is an implication, then the presence of this single case invalidates the statement. endingFrom the given examples, it is clear that the use of alternative representations of logical statements aid in logical reasoning. In fact, both Euler circles and truth tables were consistent in invalidating the logic for both examples.Question 1Let Equations firmnessModify eqn 1 Substitute to eqn 2 finale UniquePhil has 10 $0.37 stamps.Question 2Solution Using the Venn Diagra mExactly 2 writing instruments polish 15 backpacks contain exactly two of the threesome writing instruments.Question 3Question 4SolutionConclusion The car got 54.4 miles per gallon.Question 5Question 6BiconditionalQuestion 72.8700Question 8Question 9SolutionConclusion cups of flour should be used.Question 10SolutionDuring peak hours During off-peak hours Conclusion $1.76 can be saved by making 16-minute calls during off-peak hours.Question 11SolutionUsing the Law of Contraposition Using De Morgans Law Conclusion They are logically equivalent.Question 12Solution truth tablepqqpq straightTRUE ridiculousFALSETRUEFALSETRUETRUEFALSETRUEFALSEFALSEFALSEFALSETRUEFALSEConclusion There is only 1 T in the final columb.Question 13Question 14Question 15ValidQuestion 16Question 17Question 18InvalidQuestion 19Solution1 3 7 13 15 19 25 27 31 37 ---Diff 2 4 6 2 4 6