Model of Knowledge by Fitzgerald Systems

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Consider a Universal set of (U) = {1, 3, 5, 8, 10, 35, 36, 37}

• {}; set; A collection of elements; (A) = {1, 3, 5, 8}, (B) = {5, 8, 10, 35}, (C) = {8, 10, 36, 37}
• A ∪ B; union; Elements that belong to A or B; A ∪ B = {1, 3, 5, 8, 10, 35}
• A ∩ B; intersection; Elements that belong to A and B; A ∩ B = {5, 8}
• A = B; equality; Elements of set A are the same as elements of set B; {1, 2} = {1, 2}
• A ⊆ B; subset; Every element of A is also an element of B; {1, 3} ⊆ {1, 3, 5, 8, 10, 35}
• A ⊂ B; proper subset; Every element of A is also an element of B but A ≠ B; {1, 3} ⊆ {1, 3, 5, 8, 10, 35}
• A ⊄ B; negation of A ⊂ B
• A ⊇ B; superset; Every element of B is also an element of A; {1, 3, 5, 8, 10, 35} ⊇ {1, 3}
• A ⊃ B; proper superset; Every element of B is also an element of A but B ≠ A; {1, 3, 5, 8, 10, 35} ⊃ {1, 3}
• A \ B or A - B; relative complement; Elements that are members to A but not members to B; A - B = {1, 3}

<math> A^c <\math> Ac = complement

• {} or Ø; null set or empty set; A set with no elements;
• P(A); power set; Given a set A, power set of A is the set of all subsets of the set; P({a, b}) = {Ø, {a}, {b}, {a,b}}