Question

A = { a, b, c, f }
B= { c, d, e }
C= { g }
I AUB=
2 BUC=
3 AUBUC=
4 ANB=
5 CNB=​

Answer 1

Given that :-

• A = { a, b, c, f }
• B = { c, d, e }
• C = { g }

To find :-

[1] A ∪ B

[2] B ∪ C

[3] A ∪ B ∪ C

[4] A ∩ B

[5] C ∩ B

Solution :-

In the question we are given 3 different sets and we have to find union and Intersection of several sets. Before solving this problem, we should know about intersection and union of two sets.

Intersection is the common element present in both sets. Intersection of two sets say X and Y is the element which is present in both the sets X and Y.

Intersection of set X and Y is given by X ∩ Y.

Union is basically a set which contains elements of both the sets X and Y in case of union of sets X and Y.

Union of two set X and Y is given by X ∪ Y.

Now let's solve the given problem!

[1] A ∪ B = { a, b, c, d, e, f }

[2] B ∪ C = { c, d, e, g }

[3] A ∪ B ∪ C = { a, b, c, d, e, f, g }

[4] A ∩ B = { c }

[5] C ∩ B = { } or ϕ ( phi )

Additional Information :-

A set is a collection of distinct objects that are seperated by commas and are kept inside curly braces.

These objects are called the elements of the set.

{ } or also represented as ϕ called phi is an empty set which contains no element.

Important property of intersection and union :

• A ∪ B = B ∪ A
• A ∪ ϕ = A
• A ∩ ϕ = ϕ
• A ∩ B = B ∩ A