Set Operations

The four important set operations that are widely used are:

• Union of sets
• Intersection of sets
• Complement of sets
• Difference of sets

Fundamental Properties of Set operations:

Like addition and multiplication operation in algebra, the operations such as union and intersection in set theory obeys the properties of associativity and commutativity. Also, the intersection of sets distributes over the union of sets.

Sets are used to describe one of the most important concepts in mathematics i.e. functions. Everything that you observe around you, is achieved with mathematical models which are formulated, interpreted and solved by functions.

Problems and Solutions

Q.1: If U = {a, b, c, d, e, f}, A = {a, b, c}, B = {c, d, e, f}, C = {c, d, e}, find (A ∩ B) ∪ (A ∩ C).

Solution: A ∩ B = {a, b, c} ∩ {c, d, e, f}

A ∩ B = { c }

A ∩ C = { a, b, c } ∩ { c, d, e }

A ∩ C = { c }

∴ (A ∩ B) ∪ (A ∩ C) = { c }

Q.2: Give examples of finite sets.

Solution: The examples of finite sets are:

Set of months in a year

Set of days in a week

Set of natural numbers less than 20

Set of integers greater than -2 and less than 3

Q.3: If U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, A = {3, 5, 7, 9, 11} and B = {7, 8, 9, 10, 11}, Then find (A – B)′.

Solution: A – B is a set of member which belong to A but do not belong to B

∴ A – B = {3, 5, 7, 9, 11} – {7, 8, 9, 10, 11}

A – B = {3, 5}

According to formula,

(A − B)′ = U – (A – B)

∴ (A − B)′ = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11} – {3, 5}

(A − B)′ = {2, 4, 6, 7, 8, 9, 10, 11}.