1. **State the problem:** Find the disjunctive normal form (D.N.F) of the Boolean function $$f(x,y,z) = \overline{x} \overline{z} + \overline{y} \overline{z}$$. 2. **Recall the definition:** The disjunctive normal form is a sum of minterms (ANDs of literals) that cover all cases where the function is 1. 3. **Rewrite the function:** $$f = \overline{x} \overline{z} + \overline{y} \overline{z} = \overline{z}(\overline{x} + \overline{y})$$ 4. **Expand the expression to minterms:** $$\overline{z}(\overline{x} + \overline{y}) = \overline{z}\overline{x} + \overline{z}\overline{y}$$ 5. **Express each term as minterms including all variables:** - For $$\overline{z}\overline{x}$$, the variable $$y$$ can be either 0 or 1, so: $$\overline{z}\overline{x} = \overline{z}\overline{x}y + \overline{z}\overline{x}\overline{y}$$ - For $$\overline{z}\overline{y}$$, the variable $$x$$ can be either 0 or 1, so: $$\overline{z}\overline{y} = \overline{z}\overline{y}x + \overline{z}\overline{y}\overline{x}$$ 6. **Combine all minterms:** $$f = \overline{z}\overline{x}y + \overline{z}\overline{x}\overline{y} + \overline{z}\overline{y}x + \overline{z}\overline{y}\overline{x}$$ 7. **Simplify by removing duplicates:** Note that $$\overline{z}\overline{x}\overline{y}$$ and $$\overline{z}\overline{y}\overline{x}$$ are the same term, so only one is needed. 8. **Final D.N.F:** $$f = \overline{z}\overline{x}y + \overline{z}\overline{x}\overline{y} + \overline{z}\overline{y}x$$ This is the disjunctive normal form of the function. **Answer:** $$f(x,y,z) = \overline{z}\overline{x}y + \overline{z}\overline{x}\overline{y} + \overline{z}\overline{y}x$$