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

Logical Reasoning - Math Problem ExampleEuler circles early(a)wise known as Euler diagrams ar graphical representations of logical systemal statements. Each coif in this diagram is represented as a circle or closed curve. Intersections between sets are shown as partially overlapping circles. On the other hand, the equivalence of two sets is given by a complete overlap of the circles. Using this approach, the relationship of sets becomes clear. It is then easy to determine the validity of a demonstration based on the diagram.For the first statement it is clear from the diagram that given the premise, there is no established relation between B and C. Likewise, the second statement also establishes no relationship between the two. Therefore, both statements are invalid.In contrast, truth remits 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 eac h combination. While not as intuitive as Euler circles, this approach provides a more exhaustive view 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 social movement of this single case invalidates the statement.ConclusionFrom 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 reconciled in invalidating the logic for both examples. chief 1Let EquationsSolutionModify eqn 1 Substitute to eqn 2 Conclusion UniquePhil has 10 $0.37 stamps. perplexity 2Solution Using the Venn DiagramExactly 2 writing instruments Conclusion 15 backpacks con tain exactly two of the three writing instruments. psyche 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 qualification 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 tablepqqpqTRUETRUE monstrousFALSETRUEFALSETRUETRUEFALSETRUEFALSEFALSEFALSEFALSETRUEFALSEConclusion 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