Simplification (logic)
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In logic, simplification is a valid simple argument of the form:
- A and B, therefore A
or
- A and B, therefore B
or in logical operator notation:
- <math> A \and B \vdash A <math>
or
- <math> A \and B \vdash B <math>
The argument has one premise, namely a conjunction, and one often uses simplification in longer arguments to make one of the conjuncts available. As a strategy it is fairly straightforward, so much so, it may have been overlooked in the past. Since A and B implies B and A, one form of the argument can be used to derive the other. An example in English:
- It's raining and it's pouring.
- Therefore it's raining.