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The symmetric property is demonstrated by showing that if one number has the same remainder modulo 3 as another, then the second number also has the same remainder modulo 3 as the first.

Conditions: The relation is equality of remainders modulo 3.; The property requires that if x is related to y, then y is related to x.

The symmetric property is demonstrated by showing that if one number has the same remainder modulo 3 as another, then the second number also has the same remainder modulo 3 as the first.

Conditions: The relation is equality of remainders modulo 3.; The property requires that if x is related to y, then y is related to x.

The reflexive property is demonstrated by showing that any number is related to itself, specifically that 10 mod 3 is equal to 10 mod 3.

Conditions: The relation is defined as equality of remainders modulo 3.; The property requires every element to be related to itself.

The reflexive property is demonstrated by showing that any number is related to itself, specifically that 10 mod 3 is equal to 10 mod 3.

Conditions: The relation is defined as equality of remainders modulo 3.; The property requires every element to be related to itself.

Transitivity is shown by demonstrating that if the first number has the same remainder modulo 3 as the second, and the second has the same remainder as the third, then the first has the same remainder as the third.

Conditions: The relation is equality of remainders modulo 3.; The property requires that if x is related to y and y is related to z, then x is related to z.

Transitivity is shown by demonstrating that if the first number has the same remainder modulo 3 as the second, and the second has the same remainder as the third, then the first has the same remainder as the third.

Conditions: The relation is equality of remainders modulo 3.; The property requires that if x is related to y and y is related to z, then x is related to z.