Equal Sets

What is the Meaning of Equal Sets?

Two sets are regarded as equal sets when they have all the same elements and also the same number of elements.

Which symbol is used to represent Equal Sets?

Equal sets are represented with the notation ‘=’ between them as follows:

P = Q

How do you Prove Sets are Equal?

To proof any two given sets are equal sets we need to asses two things in given sets.

• Both sets needs to have same number of elements i.e., both sets have same cardinality.
• All the elements of each set are same as the other.

If any two sets hold the following two conditions, those are equal sets.

When are Two Sets Equal?

When both sets have equal number of elements and all the elements of one sets are same as other set, then both the given sets are equal.

What are Equal and Unequal Sets?

Equal sets are those which has equal number of same elements in both the sets, on the other hand if set either have unequal number of elements, different elements or both, then sets are said to be unequal.

What is the difference between Equal and Equivalent Sets?

Equal Sets are those sets whose all elements are equal and are represented with a “=” sign between two sets.

However, equivalent sets are those which have the same cardinality i.e., an equal number of elements and ‘~’ or ‘≡’ is used between two sets to represent this equivalent relation between them.

What are some Properties of Equal Sets?

Some porperties of Equal Sets are:

• If A = B, then A ⊂ B and B ⊂ A.
• If A = B then, A ∩ B = A = B.

“All Equivalent Sets are Equal Sets” is True or False.

No, all equivalent sets are not equal as equivalent sets can have different element in each other but equal sets can’t have that.

What is an Example of Equal and Unequal sets?

For sets A = {a, e, i, o, u}, B = {a, i, o, u, e} and C = {a, 1, e, 5, i}

A = B but A ≠ C and B ≠ C as well.

Thus, A and B are examples of Equal Sets, and A & C or B & C are examples of Unequal Sets.

Equal Set is the relation between two sets that tells us about the equality of two sets i.e., all the elements of both sets are the same and both sets have the same number of elements as well. As we know, a set is a well-defined collection of objects where no two objects can be the same, and sets can be empty, singleton, finite, or infinite based on the number of its elements.

Other than that, there can be sets based on the relationships between two sets such as subsets, equivalent sets, equal sets, or it can set of subsets for any set, i.e., power sets, etc. This article explores one such relationship of sets known as Equal Set, including definition, examples, properties as well as Venn diagram.