ExplanationSince a, b, and c are all multiples of 3, a = 3x, b = 3y, c = 3z, where x > y > z > 0 and all are integers.

Substitute these new expressions into the statements.

First statement: \(a + b + c = 3x + 3y + 3z = 3(x + y + z)\). Since (x + y + z) is an integer, this number must be divisible by 3.

Second statement: \(a - b + c = 3x - 3y + 3z = 3(x - y + z)\). Since (x + y + z) is an integer, this number must be divisible by 3.

Third statement:\(\frac{abc}{9}=\frac{3x \times 3y \times 3z}{9}=\frac{27xyz}{9}= 3xyz\). Since xyz is an integer, this number must be divisible by 3.

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