Question

two equivalent sets are always equal sets. is it true?

Answer 1

No, two equivalent sets are not always equal

This is because equivalent sets are those which have same cardinal number whereas equal sets have same elements in them.

Therefore, if the elements in an equivalent set is equal then it's an equal set.

For example :-

Let us consider two equivalent sets

A = {1,2} ==> n(A) = 2

B = {6,7} ==> n(B) = 2

Since, the number of elements in two sets are equal, they are equivalent but they are not equal sets, because their elements are not equal.

Case 2 :-

Let us consider two equivalent sets

A = {1,3} ==> n(A) = 2

B = {1,3} => n(B) = 2

Since the number of elements and elements are same in these sets, these sets are both equivalent and equal sets.

Answer 2

Answer:

Yes, all equal sets are also equivalent sets. Equal sets have the exact same elements, so they must have the same number of elements. Therefore, equal sets must also be equivalent. No, not all equivalent sets are also equal sets.........