Prove or disprove: if a ≡ b (mod c), then a + x ≡ b + x (mod c + x)?
∀a, b, c, x ∈ Z where x and c are positive,
if a ≡ b (mod c), then a + x ≡ b + x (mod c + x). prove using any method, or disprove using a concrete example.
More Questions From This User See All
Answers & Comments
Verified answer
Let a = 9, b = 4, c = 5, and x = 1.
9 ≡ 4 (mod 5)
If the proposition is true, then 10 ≡ 5 (mod 6).
10 - 5 = 5, and 5 is not divisible by 6.
Therefore, 10 ≡ 5 (mod 6) is not true, and the proposition is disproved by the contradiction.