Snapsolve any problem by taking a picture. Try it in the Numerade app?
5_ For natural numbers a and b, define a ~ b if and only if a2 + b is even: a_ Prove that defines an equivalence relation b. Find all equivalence classes. C. What is the partition of N determined by this equivalence relation? (ie: the quotient set)
Added by Xavier E.
Close
Step 1
Reflexivity: We need to show that a ~ a for all natural numbers a. Since a^2 is always even if a is even and odd if a is odd, a^2 + a will be even if a is even. Thus, a ~ a for all even natural numbers a. For odd natural numbers a, a^2 + a will be odd + odd = Show more…
Show all steps
Lauren Shelton and 64 other Algebra educators are ready to help you.
Ask a new question
Recommended Videos
Let A = {n ∈ Z | n is a multiple of 5, 25 < n < 25}. Define an equivalence relation on A as a ~ b if a - b is a multiple of 5. Write down all the equivalence classes for this relation. Explain why the equivalence classes create a partition for A.
Vincenzo Z.
Recommended Textbooks
Algebra and Trigonometry
Elementary and Intermediate Algebra
Watch the video solution with this free unlock.
Not finding what your looking for? Here are some other ways we can help!
Generate practice questions
Explain a concept
Create a study plan
EMAIL
PASSWORD