WHAT ARE EQUIVALENT SETS? - MATHS - 2024

A pair of sets are called "Equivalent Sets" if they have the same number of elements.

Mathematically, the definition of equivalent sets is: two sets A and B are equivalent, if they have the same cardinality, that is, if -A - = - B-.

Therefore, it does not matter what the elements of the sets are, they can be letters, numbers, symbols, drawings or any other object.

Furthermore, the fact that two sets are equivalent does not imply that the elements that make up each set are related to each other, it only means that set A has the same number of elements as set B.

Equivalent Sets

Before working with the mathematical definition of equivalent sets, the concept of cardinality must be defined.

Cardinality: The cardinal (or cardinality) indicates the number or quantity of elements in a set. This number can be finite or infinite.

Equivalence Ratio

The definition of equivalent sets described in this article is really an equivalence relation.

Therefore, in other contexts, saying that two sets are equivalent may have another meaning.

Examples of Equivalent Sets

Here is a short list of exercises on equivalent sets:

1.- Consider the sets A = {0} and B = {- 1239}. Are A and B equivalent?

The answer is yes, since both A and B only consist of one element. It doesn't matter that the elements have no relationship.

2.- Let A = {a, e, i, o, u} and B = {23, 98, 45, 661, -0.57}. Are A and B equivalent?

Again the answer is yes, since both sets have 5 elements.

3.- Can A = {- 3, a, *} and B = {+, @, 2017} be equivalent?

The answer is yes, since both sets have 3 elements. It can be seen in this example that it is not necessary for the elements of each set to be of the same type, that is, only numbers, only letters, only symbols…

4.- If A = {- 2, 15, /} and B = {c, 6, &,?}, Are A and B equivalent?

The answer in this case is No, since set A has 3 elements while set B has 4 elements. Therefore, sets A and B are not equivalent.

5.- Let A = {ball, shoe, goal} and B = {house, door, kitchen}, are A and B equivalent?

In this case the answer is yes, since each set is made up of 3 elements.

Observations

An important fact in defining equivalent sets is that it can be applied to more than two sets. For example:

-If A = {piano, guitar, music}, B = {q, a, z} and C = {8, 4, -3}, then A, B and C are equivalent since all three have the same amount of elements.

-Sean A = {- 32,7}, B = {?, q, &}, C = {12, 9, $} and D {%, *}. Then the sets A, B, C and D are not equivalent, but B and C are equivalent, as well as A and D.

Another important fact to be aware of is that in a set of elements where the order does not matter (all the previous examples), there can be no repeating elements. If there are, you only need to place it once.

Thus, the set A = {2, 98, 2} must be written as A = {2, 98}. Therefore, care must be taken when deciding whether two sets are equivalent, since cases such as the following can occur:

Let A = {3, 34, *, 3, 1, 3} and B = {#, 2, #, #, m, #, +}. You can make the mistake of saying that -A- = 6 and -B- = 7, and therefore conclude that A and B are not equivalent.

If the sets are rewritten as A = {3, 34, *, 1} and B = {#, 2, m, +}, then it can be seen that A and B are equivalent since they both have the same number of elements (4).

References

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2. Cisneros, MP, & Gutiérrez, CT (1996). Mathematics Course 1st. Editorial Progreso.
3. García, L., & Rodríguez, R. (2004). Math IV (algebra). UNAM.Guevara, MH (1996). ELEMENTARY MATH Volume 1. EUNED.
4. Lira, ML (1994). Simon and mathematics: second grade math textbook. Andres Bello.
5. Peters, M., & Schaaf, W. (nd). Algebra a modern approach. Reverte.
6. Riveros, M. (1981). Mathematics Teacher's Guide First Year Basic. Editorial Jurídica de Chile.
7. S, DA (1976). Tinker Bell. Andres Bello.