Congratulations, we have proved the reflexive property for congruences! The next property of congruences we will verify is another simple idea called the *symmetric property*. The symmetric property for congruences goes like this: if a is congruent to b mod n for integers a, b, and n with n > 0, then b must also be congruent to a mod n. To prove the symmetric property for congruences, we first suppose that a, b, and n are integers with n > 0 such that a is congruent to b mod n. In other words, we know that n divides (a-b), or that

`$(a - b) = nk$`

for some integer `k`

. Multiply both sides by -1:

`$-(a - b) = -(nk)$`

Distribute the negative on the left-hand side of the equation and move the negative sign on the right-hand side to obtain:

`$-a + b = b - a = -(nk) = n(-k)$`

Since `k`

is an integer, its negative (`-k`

) is also an integer. We have shown that n divides (b-a), and by the definition of congruence, we have proven that b is congruent to a mod n. Python is quite useful in helping us see the symmetric property in action, and the upcoming checkpoints will ask you to demonstrate this property using code.

### Instructions

**1.**

Print whether or not the following statement:

`$11 \equiv 2\;(mod\;3)$`

is true.

**2.**

Now print out whether or not:

`$2 \equiv 11\;(mod\;3)$`

is true.