Question

Let R be the relation on Z defined by aRb if a^2 - b^2 is divisible by 4. (a) Prove that R is an equivalence relation on Z. (b) What are the equivalence classes for this equivalance relation?

          Let R be the relation on Z defined by aRb if a^2 - b^2 is divisible by 4.
(a) Prove that R is an equivalence relation on Z.
(b) What are the equivalence classes for this equivalance relation?

Added by Ines G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/13/2023

Step 1

Reflexivity: For any integer a, aR a if a? a2 is divisible by 4. Since a2 is always divisible by 4 if a is even, or if a is odd and a is congruent to 1 or 3 modulo 4, we have aR a for all integers a. Show more…

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