How will you explain to a student the difference between equality and equivalence of sets?

Question

mandre · Answer

Two sets are equal if their elements are equal. Two sets are equivalent if they have the same number of elements.
A = {a, b, c} is equivalent to B={1, 2, 3} but they are not equal.
A={a, b, c} is equal to C={a, b, c}

anonymous · Answer

More specifically, an equality is the state when two sides of an equation are equal, e.g: $\bf 1+1=2$ is an equality.

Two sets A and B are equivalent when every element in set A also exists in set B and the cardinality of both sets is equal, i.e.$$\bf A \ \cup \ B =A=B \ and \ |A|=|B|$$

anonymous · Answer

Thank you!