MHB What are the definitions of memoryless, linear, and stable properties?

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Memoryless properties indicate that the future state of a system depends only on its current state, not on past states. Linear properties refer to systems where the output is directly proportional to the input, adhering to the principles of superposition. Stability implies that a system's output remains bounded for bounded inputs, ensuring predictable behavior over time. The discussion highlights the need for clear definitions and proofs related to these properties. Understanding these concepts is crucial for analyzing system behavior effectively.
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Hi, I need to prove/disprove the following statements. I am facing lots of difficulty though. Intuitively my guess is that they are all true, but I cannot begin to think how I would prove them.

I have attached the questions and appreciate any help.

Thanks.
 

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You need to apply the definitions of these properties. What are the definitions of memoryless, linear, stable?
 

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