The relation "Congruence modulo m" is:

A) reflexive only

  B) transitive only

C) symmetric only

  D) an equivalence relation

Correct Answer:
  D) an equivalence relation

Description for Correct answer:
\( \Large x=3 \left(mod\ 7\right) => x-3 = 7p,\ \left(p\ \epsilon\ I\right) \)

=> \( \Large x=7p+3,\ p\ \epsilon\ I\ i.e.,\ \{ 7p+3 : p\ \epsilon\ z \} \)

Therefore, Solution set of x is \( \Large \{ 7p + 3 : p\ \epsilon\ I \} \).

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