The Law of non-contradiction is one of the basic laws in classical logic. It states that something cannot be both true and not true at the same time when dealing with the same context. For example, the chair in my living room, right now, cannot be made of wood and not made of wood at the same time. In the law of non-contradiction, where we have a set of statements about a subject, we cannot have any of the statements in that set negate the truth of any other statement in that same set. For example, we have a set of two statements about Judas. 1) Judas hanged himself. 2) Judas fell down, and his bowels spilled out. Neither statement about Judas contradicts the other. That is, neither statement makes the other impossible because neither excludes the possibility of the other. The statements can be harmonized by stating: Judas hanged himself, then his body fell down, and his bowels spilled out.
In order to make the set of statements contradictory, we would have something like: 1) Judas hanged himself. 2) Judas did not hang himself. Since either statement excludes the possibility of the other, we would then have a contradiction since both could not be true. However, to say that Judas hanged himself and Judas fell are not contradictory since both could occur.