Question

Define (i) equal sets (ii) equivalent sets (ili) null set (iv) universal set write an example for each.


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Answer 1

Answer:

1)The equal set definition is that when two sets have the same elements. ... Equivalent sets do not have to hold the same number but the same number of elements

2)Equivalent set meaning states that two sets comprise an equal number of elements. It is not necessary to hold the same elements but include the same number of elements.

3)A set with no members is called an empty, or null, set, and is denoted ∅. Because an infinite set cannot be listed, it is usually represented by a formula that generates its elements when applied to the elements of the set of counting numbers.

4)A universal set is the collection of all objects in a particular context or theory. All other sets in that framework constitute subsets of the universal set, which is denoted as an uppercase italic letter U. The objects themselves are known as elements or members of U.

EXAMPLE:-1) and2). Equal And Equivalent Sets Examples

Equal And Equivalent Sets ExamplesIf M= {1, 3, 9, 5, −7} and N = {5, −7, 3, 1, 9,}, then it can be stated that M = N. ... Thus, it can be stated that an equivalent set is simply a set with an equal number of elements. However, the sets don't need to have the same elements but must comprise the same number of elements.

3)Any Set that does not contain any element is called the empty or null or void set. The symbol used to represent an empty set is – {} or φ. Examples: Let A = {x : 9 < x < 10, x is a natural number} will be a null set because there is NO natural number between numbers 9 and 10.

4)The universal set is a set that consists of all the elements of its subsets, including its own elements. Thus, the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Therefore, the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.