Explore BrainMass


Logic is, first and foremost, a branch of knowledge coming out of philosophy. It deals with any sort of thinking using reasoning to deduce the validity of vertain statements. For example, if one were to say A is greater than B and B is greater than C. Then, one could conclude via logic that A is greater than C. Logic with reference to mathematics refers to either applying logic to mathematical fields or applying mathematical theory to logic. Mathematical logic is then divided into four topics: set theory, proof theory, recursion theory, and model theory.


Set theory is the mathetmatical study of sets which are abstract collections of objects. An example would be the set of integers. Two of the most important concepts out of set theory are the axiom of choice and the continuum hypothesis. Proof theory takes proofs as an anstract object of mathematics and considers various analysis of them. Recursion theory is typically concerned with the links to computability, reducibility, and degrees of structure. Model theory studies the way other formal theories are modelled; that is to say how formal theories are structured in mathematics. 

Construct proofs using the eight rules of inference

Using the eight rules of inference (Simplication, Conjunction, Addition, Constructive Dilemma, Modus Ponens, Modus Tollens, Disjunctive Syllogism and Hypothetical Syllogism), construct a proof for each of the following valid arguments. A) 1. (C & ~E) > (E v T) ------- Premise 2. C ------- Premise

Proofs using Modus Pollens, Modus Tollens

Question: using the four rules of inference presented (mp,mt,ds and hs), construct a proof for the following valid argument in the answer box below. Note: A). 1. w>(pvc)..........premise 2. ~p.....................premise 3. w............./c.....premise/conclusion B). 1. H>(D<>A)......................Premise 2. Mv

Archimedes and Tub History Essay

Dear Professor, Please help me! I am in dire need of some assistance for the following: Archimedes and Tub History One of the most famous events in the study of geometry involved Archimedes and a bath tub. I need help researching this history: 1. I need at least 2-3 different sources of information. To properly compl

Venn diagram Explanation

Dear professor, I need assistance in the following: Tyrell owns a start-up company that is not yet turning a profit. As such, he is spending some of his savings every month to keep the business going. Tyrell's personal budget consists primarily of three overlapping monthly budget categories: work-related expenses, home-

Truth table for the Boolean equation

Please assist with the attached 5 problems. I've answered 1 and 3 but are not certain if they are correct. If they are not correct can you please show how to solve these problems. 1. Construct a truth table for the Boolean equation: M = A'B C' + A'B C + A B'C + A B C A B C M 0 0 0 0 0 0 1

Slack and surplus variables

. (a) Define the slack and surplus variables. What do they represent? What is (are) the difference(s) between a slack and a surplus variable? (b) Briefly describe the important parts of each step needed to make a decision using decision sciences models. (c) What are the different types of special situations that may occur

Defining Certain Subsets of the Natural Numbers

Let L be the language of addition (with equality) in first-order logic. That is, let L be the first-order language that allows for use of the equality symbol ("=") and whose only non-logical symbol is a binary function symbol "+". (That is, L has no constant symbols and no predicate (relation) symbols.) Now consider the L-str

Logic of if-then statement

I am learning about Logic in an intermediate math class. I need some help with an if then statement. So my sentence is... If the Bible is the Word of God personally delivered by God to all of humanity, then...(fill in the blank) We have been learning, The if...then statement is a common form of a logical statement. The

Discussion on relationship between causation and correlation

Describe the error in the conclusion: There is a linear correlation between the number of cigarettes smoked and the pulse rate. As the number of cigarettes increases the pulse rate increases. Conclusion: Cigarettes cause the pulse rate to increase.

Sub Annual Time Value of Money

I would like to have the solution to the following sample problems in EXCEL format so that I can see the formulas used. Thanks 1.A zero-coupon bond is a security that pays no interest, and is therefore bought at a substantial discount from its face value. If stated interest rates are 5% annually (with continuous compounding)

Computing greatest common divisor and least common multiple

1. Each row in the following table contains values for the integers a and b. In this table, the value of r is the remainder (from the Division Algorithm) when a is divided by b. Complete each row in this table by determining gcd(a, b), r, and gcd(b, r). a b gcd(a, b) Remainder r gcd(b, r) 44 12 75 21 50 33

Paying dividends to common stockholders

4. A corporation has a year end 2008 retained earnings balance of $220,000. The firm reported net profits after taxes of $50,000 in 2009 and paid dividends in 2009 of $30,000. The firm's retained earnings balance at year end 2009 is ______. A. $240,000 B. $250,000 C. $270,000 D. $300,000 29. The board of directors of th

Torque and Power

Table 1 shows a set of torque-speed measurements for a d.c. electric motor intended for use in an electric wheelchair. Data of this type is used by manufacturers to help specify motor performance. Table1 Speed /rpm..............600..........1200......1850..........2400.......3050.........3700 Torque /Nm..............5.51...

Park Pobedy station in the Moscow Metro

Park Pobedy station in the Moscow Metro contains one of the longest escalators in Europe. Each one is 120 m in length and has 740 steps, of which 350 are available (i.e. not on their way back inside the mechanism) and on the inclined section at any given moment. The height difference between the bottom and top steps is 55 m, and

Business Math Applications in the Real World

1) How can you solve for an equation of a line given the following. A. One point and the slope B. Two points C. Slope 2) When graphing a linear inequality. How do you know if the inequality represents the area above or below the line? How do you know if it also represents the points on the line? 3) Why is it true that

Logic Questions Disposable Diapers

Give a critical evaluation of each of the following passages 9. If voluntary school prayer for our children is going to make them more moral, then just think what mandatory church attendance on Sunday could do for the rest of us." (Roderick M. Boyes) 10. If the aquifer is developed by the land owners, several endangered sp

Logical reasoning

Sharky, a leader of the underworld, was killed by one of his own band of four henchmen. Detective Sharp interviewed the men and determined that all were lying except one. He deduced who killed Sharky on the basis of the following statements: a. Socko: Lefty killed Sharky. b. Fats: Muscles didn't kill Sharky c. Lefty: Muscle