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Set theory is a branch of mathematical logic that studies sets, which are collections of objects. Set theory is concerned with sets that are relevant to mathematics as a whole. Here are some definitions from set theory: Subset: If every element of is also an element of , then is a subset of. Proper subset: If is a subset of and contains something that does not contain. Equality: If and only if for any.
Set theory provides fundamental theoretical structures for other areas of mathematics.
Some concepts in set theory include: Union: The union of two sets A and B contains all the objects that are in either set. Intersection: The intersection of two sets A and B contains all the objects that are in both sets. Complementation: The complement of set A consists of all the elements that are in the universal set U but not in A.
Relations can be represented by sets of ordered pairs (a, b) where a bears a relation to b. For example, calendar years may be paired with automobile production figures, weeks with stock market averages, and days with average temperatures
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