Step-by-step Solution:

After analyzing the expression with a Karnaugh map, we find that splitting the \( xy \) term is beneficial: \[ xy + xy'z + x'yz' \] Expanding and simplifying step by step: \[ xy(1) + xy'z + x'yz' \] \[ xy(z + z') + xy'z + x'yz' \] \[ (xyz + xy'z) + (xyz' + x'yz') \] \[ xz(y + y') + yz'(x + x') \] \[ xz(1) + yz'(1) \] \[ xz + yz' \] Thus, the simplified Boolean expression is: \[ \mathbf{xz + yz'} \]