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# The relation "Congruence modulo m" is:

 A) reflexive only B) transitive only C) symmetric only D) an equivalence relation

 D) an equivalence relation

$$\Large x=3 \left(mod\ 7\right) => x-3 = 7p,\ \left(p\ \epsilon\ I\right)$$

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

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

Part of solved Set theory questions and answers : >> Elementary Mathematics >> Set theory

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