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Set Theory Notation

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\cup

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The union of two sets, containing all elements that are in either set. Used in expressions like ABA \cup B to denote a set containing all elements that are in set AA, set BB, or both.

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\cap

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The intersection of two sets, containing only the elements that are in both sets. Used in expressions like ABA \cap B to denote a set containing all elements that both sets have in common.

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\setminus

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The set difference, representing the elements that are in one set but not in the other. ABA \setminus B includes all the elements that are in AA but not in BB.

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\in

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The membership symbol, indicating that an element belongs to a set. Used in expressions like xAx \in A to state that element xx is a member of set AA.

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\subset

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The subset symbol, indicating that all elements of the first set are also elements of the second set. ABA \subset B means that every element of AA is also in BB.

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\supset

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The superset symbol, indicating that the first set contains all elements of the second one. ABA \supset B means that every element of BB is also in AA.

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\emptyset

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The empty set symbol, representing a set that contains no elements. \emptyset is the set with zero members.

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R\mathbb{R}

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The symbol for the set of real numbers, including all rational and irrational numbers.

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N\mathbb{N}

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The symbol for the set of natural numbers, which includes all positive integers starting from 1. Some definitions also include zero.

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\forall

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The universal quantification symbol, signifying 'for all' or 'for every'. Used in statements like xA,P(x)\forall x \in A, P(x) to mean that predicate PP holds true for every element xx in set AA.

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