# Discrete Math proof help please! I have to prove : if k ≡ l mod j and f ≡ g mod j then (k+f) ≡ (l+g) mod j I'm using direct proof to prove this.let's say s and t are integers...Would l = k...

Discrete Math proof help please!

# I have to prove : if k ≡ l mod j and f ≡ g mod j then (k+f) ≡ (l+g) mod j

I'm using direct proof to prove this.let's say s and t are integers...

Would l = k + sj, and g = f + tj?

If so, can you please help me out how to prove (k+f) ≡ (l+g) mod j. The mod is killing me! :(

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so l+g = k +sj + f + tj = (k+f) + (s+t)j = (k+f) mod j