By Sylvia Forman, Agnes M. Rash
The entire fact approximately entire Numbers is an advent to the sphere of quantity idea for college students in non-math and non-science majors who've studied a minimum of years of highschool algebra. instead of giving short introductions to a wide selection of subject matters, this ebook presents an in-depth creation to the sphere of quantity conception. the subjects lined are lots of these integrated in an introductory quantity concept direction for arithmetic majors, however the presentation is thoroughly adapted to satisfy the desires of basic schooling, liberal arts, and different non-mathematical majors. The textual content covers common sense and proofs, in addition to significant thoughts in quantity concept, and includes an abundance of labored examples and workouts to either essentially illustrate thoughts and assessment the scholars’ mastery of the material.
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Additional info for The Whole Truth About Whole Numbers: An Elementary Introduction to Number Theory
Example text
If the conditional statement is false, give an example that shows it is false. (b) Form the conditional q ) p and determine whether it is true or false. If the conditional statement is false, give an example that shows it is false. (c) Determine whether the biconditional statement p , q is true or false. 32. p: a is even. 33. p: The last digit of n is 0. 34. p: The last digit of n is 5. q: a is divisible by 6. q: n is even. q: n is divisible by 5. 4 Properties of the Integers 35. p: a is divisible by 3.
2. R, pictured below, is a rectangle. 5 Rules of Logic and Direct Proofs 39 A B C D Can you make a valid conclusion about sides AB and CD? If so, what? If not, why not? Solution In this case the premises do support a valid conclusion. If a conditional statement is true, then the consequence is true every time the condition is true. Since the shape R is a rectangle, the condition in the first premise is true for R. Therefore, the opposite sides AB and CD must be parallel. 5 Exercises 1–4. Factor the common factors out of the expression.
Deductive reasoning does not generalize specific examples. Instead, a deductive reasoning process begins with known facts and connects them using logic to reach a conclusion. The most important difference between inductive and deductive reasoning is that the conclusion of a deductive argument is guaranteed to be true, as long as the premises, or the initial pieces of information used in the argument, are true. If a deductive argument begins with a false premise, such as 2 + 2 ¼ 5, then correctly applying a rule of algebra by adding 1 to both sides of the equation produces the equation 5 ¼ 6.