1. **State the problem:** Apply DeMorgan's theorems to the expression $B + CD + EF$. 2. **Recall DeMorgan's Theorems:** - The complement of a sum is the product of the complements: $$\overline{A + B} = \overline{A} \cdot \overline{B}$$ - The complement of a product is the sum of the complements: $$\overline{AB} = \overline{A} + \overline{B}$$ 3. **Apply the complement to the entire expression:** We want to find $$\overline{B + CD + EF}$$. 4. **Use DeMorgan's theorem on the sum:** $$\overline{B + CD + EF} = \overline{B} \cdot \overline{CD} \cdot \overline{EF}$$ 5. **Apply DeMorgan's theorem to each product term:** $$\overline{CD} = \overline{C} + \overline{D}$$ $$\overline{EF} = \overline{E} + \overline{F}$$ 6. **Substitute back:** $$\overline{B + CD + EF} = \overline{B} \cdot (\overline{C} + \overline{D}) \cdot (\overline{E} + \overline{F})$$ **Final answer:** $$\boxed{\overline{B} \cdot (\overline{C} + \overline{D}) \cdot (\overline{E} + \overline{F})}$$ This is the expression after applying DeMorgan's theorems.