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Set theory Problems : Set theory is the branch of mathematics that learned about the sets, which are the collections of objects. Even though any type of objects can be added into a set, set theory is applied most often to objects that are related to mathematics. Here we will see the practice problems and examples of set theory.

Examples

1)Proof the A∪(B∩C)=(A∪B) ∩(A∪C) condition for the following sets.
A={2,3,6,7,8} B={1,2,5,7,8} C={1,3,7,8,10}
Solution
The given sets are A={2,3,6,7,8} B={1,2,5,7,8} C={1,3,7,8,10}
A∪(B∩C)=(A∪B) ∩(A∪C)
First solve the left side condition.
A∪(B∩C)
B∩C
It means common values of the sets B and C.
B∩C={1,7,8}
A∪(B∩C)
Now joining the A set values and set theory symbols.
A∪(B∩C)={ 1,2,3,6,7,8}
Solve right side condition.
(A∪B) ∩(A∪C)
A∪B={1,2,3,5,6,7,8}
A∪C={1,2,3,6,7,8,10}
(A∪B) ∩(A∪C)={1,2,3,6,7,8}
So A∪(B∩C)=(A∪B) ∩(A∪C).
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