Foundations of Mathematics: Set Theory and Functions Homework

This document presents a comprehensive solution to a mathematics assignment focused on set theory and functions. The solution begins with problems involving set notation, listing and set builder methods, and membership tables. It then delves into the algebra of sets, including Venn diagrams and proofs using set laws. The second part of the assignment addresses functions, exploring injectivity, surjectivity, and bijectivity. The solution includes finding pre-images, proving function properties, determining inverse functions, and plotting function curves. The assignment concludes with a proof demonstrating the relationship between injective and surjective functions when the sets have equal cardinality. The solutions are detailed and provide a clear understanding of each concept.