**A contradiction equation is never true, no matter what the value of the variable is.** In this case, the answer appears as the empty set, "{ }," or "phi" from the Greek alphabet, according to Seminole State College.

One example of a contradiction equation would be x+5 = x+2. No possible constant value for x exists to make this a true equation. There is no way to add 5 and 2 to the same number and end up with the same result. Attempting to solve this sort of reaction ends up with a clear contradiction. In this example, subtracting x from both sides yields 5=2.