# Why is this Statement correct: G implies ¬Contradiction?

## What makes a statement a contradiction?

A logical contradiction is the conjunction of a statement S and its denial not-S. In logic, it is a fundamental law- the law of non contradiction- that a statement and its denial cannot both be true at the same time. Here are some simple examples of contradictions.

## How do you prove a statement by contradiction?

The steps taken for a proof by contradiction (also called indirect proof) are:

1. Assume the opposite of your conclusion. …
2. Use the assumption to derive new consequences until one is the opposite of your premise. …
3. Conclude that the assumption must be false and that its opposite (your original conclusion) must be true.

## What is the contradiction of an implication?

To prove a statement of the form P ⇒ Q by contradiction, assume the assumption, P, is true, but the conclusion, Q, is false, and derive from this assumption a contradiction, i.e., a statement such as “0 = 1” or “0 ≥ 1” that is patently false: Assume P is true, and that Q is false. …

## What is the contradiction rule?

The contradiction rule is the basis of the proof by contradiction method. The logic is simple: given a premise or statement, presume that the statement is false. If this presumption leads to a contradiction, then the given statement must be true.

## Why is a contradiction problematic?

Contradictions are problematic in these theories because they cause the theories to explode—if a contradiction is true, then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise the axioms of the logic so that self-contradictory statements do not appear.