a$.$ Delve into the fundamental assumptions that underlie Prof. Walters's theory of irrelevance. Provide a detailed and comprehensive analysis of these assumptions, highlighting their significance and implications within the context of financial theory. Explain how these assumptions shape and influence the theory's conclusions and its relevance to real$-$world financial decision$-$making.

b$.$ Examine the various compelling reasons that drive a company's decision to hold cash in the short run. Provide a thorough and comprehensive discussion of the factors, circumstances, and considerations that lead companies to maintain cash reserves. Explore the multifaceted nature of short$-$term cash management, including its significance, potential advantages, and implications for a company's financial stability and operations.