MAT237Y1 : mat237 1-2Logic-Topology.pdf

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Set notations and operations (see optional reading postings) can be thought of as a translation of symbolic logic into the language of sets. Symbolic logic is about properties like p (x) which is a statment about a variable x. To say that the property p holds true for the variable x is to say p (x) is true, or sometimes just to say p (x). Now if we de ne s = {x : p (x)} then to say p is true of x is to say x s. therefore truth of a statement is translated to the membership, and x s. To say that p is not true of x is to say x 6 s, which mean x s c (s c stands for the complement of s. ) So, the negation of logic is represented by the complement operation on sets.

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