Set operations

The basic

1. Union of Sets: Union of Sets A and B is defined to be the set of all those elements which belong to A or B or both and is denoted by A∪B.

A∪B = {x: x ∈ A or x ∈ B}
Example: Let A = {1, 2, 3}, B= {3, 4, 5, 6} A∪B = {1, 2, 3, 4, 5, 6}.

Sets Operations 2. Intersection of Sets: Intersection of two sets A and B is the set of all those elements which belong to both A and B and is denoted by A ∩ B.

A ∩ B = {x: x ∈ A and x ∈ B}
Example: Let A = {11, 12, 13}, B = {13, 14, 15} A ∩ B = {13}.

Sets Operations 3. Difference of Sets: The difference of two sets A and B is a set of all those elements which belongs to A but do not belong to B and is denoted by A - B.

A - B = {x: x ∈ A and x ∉ B}
Example: Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6} then A - B = {3, 4} and B - A = {5, 6}

Sets Operations 4. Complement of a Set: The Complement of a Set A is a set of all those elements of the universal set which do not belong to A and is denoted by Ac.

Ac = U - A = {x: x ∈ U and x ∉ A} = {x: x ∉ A} Example: Let U is the set of all natural numbers. A = {1, 2, 3} Ac = {all natural numbers except 1, 2, and 3}.

Sets Operations 5. Symmetric Difference of Sets: The symmetric difference of two sets A and B is the set containing all the elements that are in A or B but not in both and is denoted by A ⨁ B i.e.

A ⨁ B = (A ∪ B) - (A ∩ B)
Example: Let A = {a, b, c, d} B = {a, b, l, m} A ⨁ B = {c, d, l, m}

Sets Operations