Purchase Solution

contrapositive

Not what you're looking for?

Ask Custom Question

Let K be a field and let f(x) in K[X] be a polynomial whose degree is either 2 or 3. Show that f(x) is irreducible if and only if it has no roots.

Purchase this Solution
Solution Summary

This solution shows how to solve a linear algebra problem.

Solution Preview

Let K be a field and let f(x) in K[X] be a polynomial whose degree is either 2 or 3. Show that f(x) is irreducible if and only if it has no roots in K.

Proof: Let K be a field and let f(x) in K[X] be a polynomial whose degree is either 2 or 3.
(=>) Suppose f(x) is reducible in K[x]. Then there exist non-constant ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Negation Mathematics

    An implication and its contrapositive are equivalent statements. When proving a theorem, it is often more convenient or more intuitive to prove the contrapositive instead.

  • Implication Equivalent to its Contrapositive: Example Problem

    253843 Implication Equivalent to its Contrapositive: Example Problem Give an example, in English, where it is true that an implication is always equivalent to its contrapositive.

  • Antecedent, Consequent, Converse, Inverse and Contrapositive

    Contrapositive = If I will not study my Math then I go to the movie. The expert examines converse, inverse and contrapositive. A Complete, Neat and Step-by-step solution is provided.

  • Examples of contrapositives conjectures, & counterexamples

    Since the contrapositive shares the same truth value as the original statement, then the original statement is also true since the contrapositive is true. 2.

  • horizontal line test

    (a) Note the contrapositive of the definition of one-to-one function given on page 136 of the text is: if a b then f(a) f(b). As we know, the contrapositive is equivalent to, (another way of saying) the definition of one-to-one.

  • Statement: If two lines are parallel then they do not intersect.

    True Converse: If 2 lines do not intersect then they are parallel False Inverse: If 2 lines are not parallel then they intersect False Contrapositive: If 2 lines do intersect then they are

  • Truth Table: Determine Whether the Two Statements Are Equivalent

    Since p-->q is equivalent to ~q --> ~p, we can obtain the contrapositive of the statement as follows. If he is not vacationing in England, then he is working in China.

  • Discrete math questions

    Note the contrapositive of the definition of one-to-one function given on of the text is: If a ≠ b then f(a) ≠ f(b). As we know, the contrapositive is equivalent to (another way of saying) the definition of one-to-one. a.

  • Various

    Remember, a contrapositive is formed by negating both the premise and the conclusion and then switching their order. For example, the contrapositive of A ---> B is ~B ---> ~A.

  • Determine Truth Value for Propositions

    The contrapositive of l --> m is ~m --> ~l. A statement and its contrapositive are logically equivalent. So, if l --> m is true, then ~m --> ~l is true. Solutions to three symbolic logic problems are given.

View More Related Solutions