Question

prove that A intersection B is a proper subset of A​

Answer 1

Step-by-step explanation:

Suppose A and B are sets. Prove that A ⊆ B if and only if A ∩ B = A.

Here's how I see it being proved.

If A and B are sets,and the intersection of A and B is equal to A, then the elements in A are in both the set A and B. Therefore, the set of A is a subset of B since all the elements are contained in the interesection of sets A and B are equal to A.

Can I prove it that way?

Answer 2

Answer:

A∩B is a proper subset of A is proved.

Step-by-step explanation:

Proper subsets:-

• A set which contains a few elements of the original set is known as the proper set.
• The symbol ⊂ is used to denote the proper set.

Step 1 of 1

To prove:-

A∩B is a proper subset of A, i.e., A∩B ⊂ A.

As we know,

A∩B is the set of all those elements that belongs to both set A and set B.

Mathematically,

A∩B = {x : x ∈ A, x ∈ B}

This implies,

All the elements of A∩B is contained in A.

⇒ A∩B ⊂ A.

Hence, A∩B is a proper subset of A is proved.

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