Union of set: Let A and B be subsets of a set X. The union of A and B is the set of all elements belonging to A or B.
Notation: “A ⋃ B” denotes “A union B” or the union of sets A and B.
Thus, A ⋃ B = {x ∈ X | x ∈ A or x ∈ B}. Or A ⋃ B = {x | x ∈ A Ú x ∈ B}.
Let A = {2,4,5} and B = {1,4,6,8}.
Then, A ⋃ B = {1,2,4,5,6,8}
Given sets A and B. x ∈ A ⋃ B if and only if x ∈ A or x ∈ B.
difference of set: Let A and B be subsets of a set X. The set B – A, called the difference of B and A, is the set of all elements in B which are not in A.Thus, B – A
Examples:
Let B = {2,3,6,10,13,15} and A = {2,10,15,21,22}.
Then B – A = {3,6,13}.
= {x ∈ X | x ∈ B and x ∉ A}.
complement of set: If A ⊂ X, then X – A is sometimes called the complement of A with respect to X.
Notation: The following symbols are used to denote the complement of A with respect to X:
∁xA, and A ‘
Thus, ∁xA = {x ∈ X | x ∉ A}.
II. PROPERTIES OF UNION, INTERSECTION, AND COMPLEMENTATION.
Theorem: Let X be an arbitrary set and let P(X) be the set of all subsets of X. P(X) is called the power set of X. Let A, B, and C be arbitrary elements of P(X).
a. A ⋂ B = B ⋂ A (Commutative Law for Intersection)
A ⋃ B = B ⋃ A (Commutative Law for Union)
b. A ⋂ (B ⋂ C) = (A ⋂ B) ⋂ C (Associative Law for Intersection)
A ⋃ (B ⋃ C) = (A ⋃ B) ⋃ C (Associative Law for Union)
এই লেকচারের পরের পেইজে যেতে নিচের 
…. তে ক্লিক কর।