Question

what is the difference between equivalent and equal sets ??​

Answer 1

Equivalent sets are sets in which the number of elements are equal.

Ex:- Set A={1,2,3}  and Set B={4,5,6} are equivalent but not equal.

Equal sets are sets in which not only the number of elements are equal, but also the elements in first set is equal to its corresponding element in the second set.

Ex:- Set A={1,2,3} and Set B={1,2,3} are equivalent as well as equal.

So, all equal sets are equivalent but not all equivalent sets are equal.

Answer 2

Definition of a Set

Before we get into the definition of an equivalent set, we need to first know what a set is. A set is a collection of elements that are usually related. They are indicated with brackets: { }. We can have a set containing numbers, words, or even pictures. Here are some examples of sets:

{January, March, May, November}

{1, 2, 3, 4, 5, 6}

When a set continues on for infinity, the last element in the set is followed by three dots known as an ellipsis, which indicates that the numbers continue. An example is shown here: {1, 2, 3, 4, 5, 6. . . }.

Equal and Equivalent Sets

When we have two sets that have the exact same elements, we call them equal sets. It does not matter what order the elements are in. It just matters that the same elements are in each set. Here are some examples of equal sets:

{1, 3, 5, 7} and {7, 5, 3, 1}

{January, March, May, November} and {May, March, January, November}

An equivalent set is simply a set with an equal number of elements. The sets do not have to have the same exact elements, just the same number of elements. Let's take a look at some examples:

Example 1

Set A: {A, B, C, D, E}

Set B: {January, February, March, April, May}

Even though Sets A and B have completely different elements (Set A comprises letters, and Set B comprises months of the year), they have the same amount of elements, which is five. Set A contains five letters and Set B contains five months. That makes them equivalent sets!

Example 2

Set C: {Sweater, Mittens, Scarf, Jacket}

Set D: {Apples, Bananas, Peaches, Grapes}

Set C and Set D both comprise word elements in completely different categories (Set C comprises articles of clothing you would wear when cold, and Set D comprises types of fruit), but they both have the same amount of elements, which is four. That makes them equivalent sets!

Example 3

See the attachment for example 3.