what is equal and equivalent set
Equal sets are two sets that have the same elements, regardless of their order or how many times they occur. For example, {1, 2, 3} is equal to {3, 2, 1} because they have the same three elements.
Equivalent sets are two sets that have the same number of elements. They may or may not have the same elements. For example, {1, 3, 5} is equivalent to {2, 4, 6} because they both have three elements. However, they are not equal because they do not have any common elements.
Equal sets are sets that contain exactly the same elements, regardless of the order or repetition of the elements. Two sets A and B are equal if every element of A is also an element of B, and every element of B is also an element of A. We write A = B.
Equivalent sets, on the other hand, are sets that have the same number of elements (or same cardinality) but not necessarily the same elements. Two sets A and B are equivalent if there exists a one-to-one correspondence (or bijection) between the elements of A and the elements of B. We write A ≈ B.
In summary, equal sets have the same elements, while equivalent sets have the same number of elements but not necessarily the same elements themselves.