Reading material for Posets and Partitions.

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I am currently pursuing a course on Discrete Mathematics(DM). The book that my instructor suggested is K.H.Rosen DM. But in today's lecture, he gave a very descriptive talk on POSETS, Lattices, Chains and Anti-Chains, and Partitions. I tried to look up the topics in K.H.Rosen, Naive Set Theory, and Introductory Combinatorics but I did not find the relevant material in any of these. I am just an UnderGraduate so rather than very specific books I would like to read texts that is sort of easy. Could anyone suggest some?

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Introduction to Lattices and Order
Book by B. Davey and H. A Priestley