Question

If A = { 1,2,3 } , B = { 3,4,5 } then A∪B = ?​

Answer 1

Union - Sets

A well-defined collection of objects is called set. The object in a set are called its member or elements. Whose elements are fixed and cannot vary.

• lt means the set doesn't change from person to person.

• Like for example, the set of natural numbers up to 5 will remain the same as {1,2,3,4,5}.

In the case of union, all the elements are included in the result. To find the union of two sets, we take all the elements of both sets such that no elements is repeated.

$\implies \rm{A \cup B = \{1,2,3,4,5\}}$

Hence, the answer is {1, 2, 3, 4, 5}.

$\rule{90mm}{2pt}$

MORE TO KNOW

1. Union.

• The union of two sets which consists of all the elements of A and B. The symbol of union is ∪.

2. Intersection.

• The intersection of two sets consists of all the elements which are common to A and B. The symbol of intersection is ∩.

1. Commutative Laws.

• A ∪ B = B ∪ A
• A ∩ B = B ∩ A

2. Associative Laws.

• (A ∪ B) ∪ C = A ∪ (B ∪ C)
• (A ∩ B) ∩ C = A ∩ (B ∩ C)

3. Distributive Laws.

• A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
• A ∩ (B∪C) = (A ∩ B) ∪ (A ∩ C)

Answer 2

Relation and Function - Union Set

It is defined as the set that consists of all elements belonging to either set A or set B or both.

Now let's move on finding the solution for our question,

Given :

• A = {1, 2, 3}
• B = {3, 4, 5}

To find :

• A∪B (A union B)

Solution :

Union is a collection of sets of all elements in the collection.

A∪B = {1, 2, 3} ∪ {3, 4, 5}

→ {1, 2, 3, 4, 5}

Hence, A∪B = {1, 2, 3, 4, 5}.

More Info :

1) Set = { }

• Eg : A = {1, 2, 3} B = {3, 4, 5

2) Intersection = '∩'

• Eg : A = {1, 2, 3} and B = {3, 4, 5}
• → A∩B = {3}

3) Proper set = '⊂'

• Eg : {1} ⊂ A

4) Universal set = 'U'

5) Is a member = '∈'

• Eg : 2 ∈ A

6) Is not a member = '∉'

• Eg : 3 ∉ A

7) Empty/Null set = 'Ø'

• Eg : {1, 2} ∩ {3, 4} = Ø