Mathematics

The key insight here is recognizing De Morgan's Laws: complement and union/intersection operations swap when you distribute a complement across them. For each expression, identify what region you're shading by first understanding what the inner operation captures, then determining what "complement" or "outside" means. Notice that $(A \cup B)′ = A′ \cap B′$ and $(A \cap B)′ = A′ \cup B′$—these pairs are actually equivalent, so their diagrams should look identical. Shade carefully to show which parts of the universal set belong to each final set.

The key insight here is recognizing De Morgan's Laws: complement and union/intersection operations swap when you distribute a complement across them. For each expression, identify what region you're shading by first understanding what the inner operation captures, then determining what "complement" or "outside" means. Notice that $(A \cup B)′ = A′ \cap B′$ and $(A \cap B)′ = A′ \cup B′$—these pairs are actually equivalent, so their diagrams should look identical. Shade carefully to show which parts of the universal set belong to each final set.