Final Exam Essay Project

MA 120 Final Exam Essay Project

Question 1

The jurors primarily employ inductive reasoning when deciding such a case. The justification for this is that inductive reasoning allows for broad generalizations based on various observations. Decision making is dependent on data and conclusions based on this data. As a result, when jurors make the final verdict, they analyze the available evidence first. With this in mind, inductive reasoning is most suited for concluding whether the defendant is guilty or not.

Question 2

We employ estimation in varying aspects of our daily life. For instance, in times when we are required to add two numbers mentally, we often round off each number and then add the rounded numbers. Despite this being a contemporary example of the application of estimation in our everyday life, more clear examples exist.  For instance, before going shopping, we often estimate the amount needed for each commodity to remain within the budget. By keeping a rough estimate of the price for each item bought, then one can maintain the total expense.

In addition, I often estimate my school expenses at the beginning of my school year. In this way, I can request the approximate amount needed for the entire year. Estimation also helps in planning for the academic year.

Question 3

The last digit of my phone number is 6.

Set A = {1,2,3,4,5,6}

The cardinality of the set

This set has various subsets

The subset of even numbers E={2,4,6}

The subset of odd numbers O={1,3,5}

The subset of multiples of 3 T={3,6}

The empty set and the set A are also subsets of A. Therefore; A has 5 subsets. E, O, and T are proper subsets of A. A proper subset B of A is such that all the elements in B are contained in A, but A contains at least 1 element which is not in B.

Question 4

My favorite numbers are 5 and 9. My initials are E, J, M. Therefore, the two sets are:

B={5,9}

C={E,J,M}

The cross product of the two sets

Question 5

Those who enjoy watching are in set A while those who enjoy watching documentary movies are inset B. In the poll, 13 people stated they enjoy watching action movies. In contrast, 9 respondents stated that they prefer watching documentary movies. Three people said that they enjoy watching both types of movies.

Question 6

We shall use the following two statements in this case:

p: Jane eats tacos

q: Peter drinks juice

1. Jane eats tacos and peter drinks juice. In mathematical notation, this is written as p^q. This statement can only be true if the two elements, p and q, are also correct.
2. Jane does not eat tacos ~p
3. Jane eats tacos or peter drinks juice.
4. If Jane eats tacos, then Peter drinks juice. When the first condition is not fulfilled, then this statement is false.
5. If Jane eats tacos, then peter drinks juice, and if Peter drinks juice, then jane eats tacos.
6. X>9. It is an example of a statement with a quantifier. The negation of this statement is .

Question 7

In logic, negations are also referred to as logical compliments. The logical contradiction is an operation in which the result is correct when the operand is false and false when the operand is right. It is worth remembering that a statement is true, then the negation is false. On the other hand, the negation is true when the report is false. To define the complement of a set, let X be a set contained in the universal set U. The addition of A refers to the elements in U that are not members of A.

Question 8

Logic is an effective method to employ in convincing someone to buy an item. The use of logic in advertising is rather widespread. For instance, insurance companies use logic implying cost savings to persuade their customers to purchase policies.  Additionally, telecommunication companies use a similar strategy to attract subscribers. A customer has to be convinced that by switching to a particular service provider, they will save funds. An example of such an advert is one by Geico. The company tells subscribers that “If you endeavor to save 15% and more, just switch to Geico.”  Peter Pan Peanut Butter also uses the marketing phrase that “If you believe in peanut butter, you gotta believe in Peter Pan.”

Question 9

The following system of linear equations has no solution:

Without employing the graphical method, it is clear that the gradient of both lines is -3.  Therefore, the two lines are parallel to each other. Since the y-intercepts of both lines are not equal, then the two lines assume different positions on top of each other. It means that this system of equations has no solution. If a system of linear equations has no solutions, no matter what value of the independent variable is plugged in, the two will always lead to a contradiction.