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This lecture delves into the semantics of loops, starting with the basic concepts and gradually moving towards more complex examples, such as a while loop that sums up a decreasing sequence of numbers. The instructor explains how to represent statements using relations, extend this representation for loops, and apply the transitive closure operation. By analyzing the conditions and updates within the loop, the lecture demonstrates how to systematically compute the meaning of a while loop and highlights the importance of constructing closed-form formulas for loop semantics.