QuestionQuestion

Problem 1
Let ∗ be a binary operation on set of rational number Q defined as follows: a∗b=a+b+2ab, where a, b ∈ Q,
a) Prove that ∗ is commutative, associative algebraic operation on Q.
b) Find the identity element if any. Solution.
c) Find the zero element if any .
d) Find all invertible elements if any

Problem 2.
a) Verify that the relation defined on set of integers Z by R7 ={(m,n) | 7 divides (m³ −n³)}⊂Z×Z is equivalence relation CLARIFICATION NOTE: (m³ same as m to the POWER OF 3)
b) Describe equivalence classes of relation R7.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    $30.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Mathematics - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats