Question

Let Q and R be any two sets given, prove that [Q̅ ∪ (Q − R)][overlined] = Q ∩ R.

Answer 1

$\overline{\left[ \overline{Q}\cup \left( Q-R \right) \right] }=\overline{\left[ \overline{Q}\cup \left( Q\cap \bar{R} \right) \right] }=\overline{\left[ \left( \overline{Q}\cup Q \right) \cap \left( \overline{Q}\cup \overline{R} \right) \right] }=\\=\overline{\left[ T\cap \left( \overline{Q}\cup \overline{R} \right) \right] }=\overline{\overline{Q}\cup \overline{R}}=Q\cap R$