Question

If `A´ subset `B´ A intersection of B?

Answer 1

Answer:

if A ⊆ B then A ∩ B = A

Step-by-step explanation:

If A ⊆ B , then x ∈ A ⇒ x ∈ B ; but not conversely

A subset B means the elements present in A are also present in B along with the elements already present in B. A intersection B means the elements common to both the sets. Then A intersection B gives A

Let x ∈ A ∩ B

then x ∈ A and x ∈ B

since A ⊆ B , x ∈ A ⇒ x ∈ B

hence x ∈ A ∩ B ⇒ x ∈ B

therefore , if A ⊆ B then A ∩ B = A

Answer 2

Answer:

If A is a subset of B then A∩B is the entire set A.

Step-by-step explanation:

It is given that A is a subset of B, when a set is subset of another set it means that one subset is entirely contained in another.

Here it means that set A is entirely contained in B, which means that all the elements of set A are present in the set B.

The intersection of two sets gives us the common elements of both the sets, intersection between two sets is denoted by ∩

Since A is a subset of B according to the above explanation, A∩B=A

which means that intersection of A and B gives us the entire set A because all the elements in A are also present in B.