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Boolean De Morgan

De Morgan’s law

Section titled “De Morgan’s law”

De Morgan’s law can help us simplify expressions which have lots of NOTs in them. It says that if we have a NOT of an AND, we can rewrite it as an OR of NOTs, and if we have a NOT of an OR, we can rewrite it as an AND of NOTs.

If you’d like a less wordy explanation of it, we ‘break the line and change the sign’, so, for example, becomes .


Like all boolean identities, we can use this in both directions, so we can also say that and .

Using it to simplify expressions

Section titled “Using it to simplify expressions”

It’s most useful when we have an expression with two NOTs ‘on top’ of each other, for example, in this example:

Simplify

Section titled “Simplify ”
  • Use De Morgan’s law to break the line and change the sign:
  • Now we have two NOTs on top of each other, so we can simplify them, using the fact that (see double negation):
  • So the final, simplified expression is .