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Symbol: \(\cup\)\nDefinition: The union of sets A and B, denoted by \(A \cup B\), is the set of elements which are in A, in B, or in both.

Symbol: \(\bar{A}\) or \(A^c\)\nDefinition: The complement of set A, denoted by \(\bar{A}\) or \(A^c\), is the set of all elements in the universal set that are not in A.

Symbol: \(\subset\)\nDefinition: Set A is a proper subset of set B, denoted by \(A \subset B\), if A is a subset of B and A is not equal to B.

Definition: Two sets A and B are said to be disjoint if they have no elements in common, i.e., if their intersection \(A \cap B\) is the empty set \(\emptyset\).

Symbol: \(-\) or \(\setminus\)\nDefinition: The difference of sets A and B, denoted by \(A - B\) or \(A \setminus B\), is the set of elements that are in A but not in B.

Symbol: \(\triangle\)\nDefinition: The symmetric difference of sets A and B, denoted by \(A \triangle B\), is the set of elements which are in either of the sets A or B but not in their intersection.

Symbol: \(\cap\)\nDefinition: The intersection of sets A and B, denoted by \(A \cap B\), is the set of all elements that are both in A and in B.

Symbol: \(\mathcal{P}(A)\)\nDefinition: The power set of A, denoted by \(\mathcal{P}(A)\), is the set of all possible subsets of A, including the empty set and A itself.

Symbol: \(\subseteq\)\nDefinition: Set A is a subset of set B, denoted by \(A \subseteq B\), if every element of A is also an element of B.