Explanation:

Discrete Time System:
A discrete time system is a system that operates on discrete time signals, where the input and output signals are sequences of numbers defined at discrete time instants.

Causality:
In signal processing, causality refers to whether the output of a system depends only on past and present values of the input, and not on future values. A causal system is one where the output at any given time depends only on the input values up to that time.

Given Discrete Time System:
The given discrete time system is described by the equation:
y[n] = x[n - 3]

Explanation of the Given System:
The equation y[n] = x[n - 3] represents a system where the output y[n] is determined by the input x[n] delayed by 3 time units. This means that the output at any time instant n is determined by the input at the time instant n - 3.

Analysis of Causality:
To determine the causality of the system, we need to consider if the output depends only on past and present values of the input.

Case 1: n < />
For n < 3,="" the="" input="" x[n]="" has="" values="" for="" n="" />< 3,="" but="" the="" output="" y[n]="" depends="" on="" x[n="" -="" 3].="" since="" the="" output="" depends="" on="" future="" values="" of="" the="" input,="" the="" system="" is="" not="" causal="" for="" n="" />< />

Case 2: n >= 3
For n >= 3, the input x[n] has values for n >= 3, and the output y[n] depends on x[n - 3]. In this case, the output only depends on past and present values of the input, satisfying causality. Therefore, the system is causal for n >= 3.

Conclusion:
Based on the analysis, we can conclude that the given discrete time system y[n] = x[n - 3] is anti-causal because it depends on future values of the input for n < 3,="" violating="" the="" causality="" condition.="" 3,="" violating="" the="" causality="" />