Step 1: Concept Slip occurs on the most densely packed planes and in the most densely packed directions within a crystal lattice.
Step 2: Meaning Densely packed planes have the largest interplanar spacing and require the least amount of shear stress to initiate dislocation movement.
Step 3: Analysis In the Face-Centered Cubic (FCC) system, the closest-packed planes are the octahedral planes.
Step 4: Conclusion These close-packed planes are represented by the Miller indices $\{111\}$.
Final Answer: (B)