Memory-less System:
A memory-less system is one where the output at any given time depends only on the input at that particular time. In other words, the output does not depend on any previous or future inputs. To determine if a system is memory-less, we need to check if the output at a specific time can be determined solely based on the input at that time.

Time-Invariant System:
A time-invariant system is one where the input-output relationship remains constant over time. In other words, if the input is delayed or advanced in time, the output should also be delayed or advanced by the same amount. To determine if a system is time-invariant, we need to check if delaying or advancing the input signal results in a corresponding delay or advancement of the output signal.

Linear System:
A linear system is one that satisfies the principles of superposition and scaling. Superposition means that if two inputs x1[n] and x2[n] produce outputs y1[n] and y2[n] respectively, then the input x[n] = a1*x1[n] + a2*x2[n] should produce the output y[n] = a1*y1[n] + a2*y2[n]. Scaling means that if an input x[n] produces an output y[n], then scaling the input by a constant factor a should result in scaling the output by the same factor. To determine if a system is linear, we need to check if it satisfies both the principles of superposition and scaling.

Causal System:
A causal system is one where the output at any given time depends only on past and present inputs, but not on future inputs. In other words, the output does not depend on any future inputs. To determine if a system is causal, we need to check if the output at a specific time can be determined solely based on the past and present inputs.

Stable System:
A stable system is one where bounded inputs produce bounded outputs. In other words, if the input to a stable system is bounded, then the output should also be bounded. To determine if a system is stable, we need to check if bounded inputs result in bounded outputs.

Analysis of the System:

To determine whether the given system Y[n] = £ is memory-less, time-invariant, linear, causal, and stable, we need to analyze its properties.

Memory-less:
A system is said to be memory-less if the output at any given time depends only on the input at that particular time. In this case, the output Y[n] is represented by the symbol £, which does not provide any information about the input. Therefore, we cannot determine whether the system is memory-less or not based on the given information.

Time-Invariant:
To determine if the system is time-invariant, we need to check if delaying or advancing the input signal results in a corresponding delay or advancement of the output signal. Since the output Y[n] is represented by the symbol £, which does not provide any information about the input, we cannot determine if the system is time-invariant or not.

Linear:
To determine if the system is linear, we need to check if it satisfies the principles of superposition and scaling. However, since the output Y[n] is represented by the symbol £, which does not provide