<P> However, that means x ∉ A c ∪ B c (\ displaystyle x \ not \ in A ^ (c) \ cup B ^ (c)), in contradiction to the hypothesis that x ∈ A c ∪ B c (\ displaystyle x \ in A ^ (c) \ cup B ^ (c)), </P> <P> therefore, the assumption x ∉ (A ∩ B) c (\ displaystyle x \ not \ in (A \ cap B) ^ (c)) must not be the case, meaning that x ∈ (A ∩ B) c (\ displaystyle x \ in (A \ cap B) ^ (c)). </P> <P> Hence, ∀ x (x ∈ A c ∪ B c → x ∈ (A ∩ B) c) (\ displaystyle \ forall x (x \ in A ^ (c) \ cup B ^ (c) \ rightarrow x \ in (A \ cap B) ^ (c))), </P> <P> that is, A c ∪ B c ⊆ (A ∩ B) c (\ displaystyle A ^ (c) \ cup B ^ (c) \ subseteq (A \ cap B) ^ (c)). </P>

State and prove de morgan's law for two sets