Implication (logic) - Simple English Wikipedia, the free encyclopedia

Implication (also known as logical consequence, implies, or If ... then) is a logical operation. It is the relationship between statements that holds true when one logically "follows from" one or more others. While a statement of the form "if P then Q" is often written as , the assertion that "Q is a logical consequence P" is often written as .[1][2]

Implications take two arguments. It returns false if and only if the first term is true and the second term is false.[2]

This may be problematic, because it means that from a false proposition, anything can follow.

Examples

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The following shows a (valid) implication

  1. All humans are mortal (they die).
  2. Aristotle is human.
  3. Therefore, Aristotle is mortal.

On the other hand, the statement I promise that if I am healthy, I will come to class has four possibilities:

  1. I am healthy, and I do come to class. I have kept my promise.
  2. I am healthy, and I do not come to class. I have not kept my promise.
  3. I am not healthy, and I do come to class. I have kept my promise.
  4. I am not healthy, and I do not come to class. I have kept my promise.

In the second scenario, the statement is false, since the promise is broken. In other scenarios, the statement is true, since the promise is kept.

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References

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  1. "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-09-04.
  2. 2.0 2.1 Weisstein, Eric W. "Implies". mathworld.wolfram.com. Retrieved 2020-09-04.