<P> Working in the opposite direction, the second expression asserts that A is false and B is false (or equivalently that "not A" and "not B" are true). Knowing this, a disjunction of A and B must be false also . The negation of said disjunction must thus be true, and the result is identical to the first claim . </P> <P> The application of De Morgan's theorem to a conjunction is very similar to its application to a disjunction both in form and rationale . Consider the following claim: "it is false that A and B are both true", which is written as: </P> <Dl> <Dd> ¬ (A ∧ B). (\ displaystyle \ neg (A \ land B).) </Dd> </Dl> <Dd> ¬ (A ∧ B). (\ displaystyle \ neg (A \ land B).) </Dd>

What is de morgan's theorems explain with an example