Set Operations

• The union operation will result into a new set.
• Operands are the sets involved in the union or intersection of sets.
• The union of two sets, denoted by the symbol ∪, is a set containing all distinct elements from both sets.

  
• Intersection of sets is an operation will result into a new set that are common to the operands.
• The intersection of sets is a set operation denoted by the symbol ∩.

  
• Complement operator results to a new set that is not found in a given set with respect to a particular universal set. It can be denoted as A' or A^c or Ā.

  
• The difference operand is denoted by the minus symbol that would result to a new set containing the elements of A that are not in B.

  
• How is this read as? ∧

  It is read as "and".
• Symmetric Difference operand is denoted with the XOR or triangle symbol. It is the set: (A-B)U(B-A)

  
• V what does this logical operator mean?

  The logical operator "V" represents the logical OR operation. It returns true if at least one of the operands is true.
• An element x belongs to the union of the sets A and B if and only if x belongs to A or x belongs to B.

  
• If A and B are disjoint, then their intersection is the empty set.
• The cardinality of two union finite sets is |A|+|B| - |A ∩ B|

  
• Difference of sets A and B is denoted as A-B. This is also called the complement of B with respect to A.

  
• The complement of the set A is the complement of A with respect to its Universal set. Therefore, the complement of the set A is U-A.

  
• What set identity is this?

  Answer: Identity Laws

  
• What set identity is this?

  Answer: Domination laws

  
• What set identities is this?

  Answer: Idempotent laws

  
• What set identity is this?

  Answer: Complementation law

  
• What set identity is this?

  Answer: Commutative law

  
• What identity law is this?

  Answer: Associative law

  
• What set identity is this?

  Answer: Distributive law

  
• What set identity is this?

  Answer: De Morgan's law

  
• What identity law is this?

  Answer: Absorption law

  
• What identity law is this?

  Complement law

  
• Multiset is an unordered collection of elements where an element can occur as a member more than once.
• To avoid ambiguity, there is an alternate notation for multiset. Which denotes that a1 is occurring m1 times.

  
• Multiplicity of an element in a multiset is how many times an element appears in a multiset.