Question

identify the the following type of sets. 1) A is the set of Negative rational number. a) singletonset b) empty set c) infinite set d) finite set​

Answer 1

Answer:

Since, a Set is a well – defined collection of objects; depending on the objects and their characteristics, there are many types of Sets which are explained with suitable examples, as follows: –

Empty or Null or Void Set

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. Therefore, A = {} or φ

Let W = {d: d > 8, d is the number of days in a week} will also be a void set because there are only 7 days in a week.

Answer 2

Answer:

Since, a Set is a well – defined collection of objects; depending on the objects and their characteristics, there are many types of Sets which are explained with suitable examples, as follows: –

Empty or Null or Void Set

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. Therefore, A = {} or φ

Let W = {d: d > 8, d is the number of days in a week} will also be a void set because there are only 7 days in a week.Finite and Infinite Sets

Any set which is empty or contains a definite and countable number of elements is called a finite set. Sets defined otherwise, for uncountable or indefinite numbers of elements are referred to as infinite sets. Examples:

A = {a, e, i, o, u} is a finite set because it represents the vowel letters in the English alphabetical series.

B = {x : x is a number appearing on a dice roll} is also a finite set because it contains – {1, 2, 3, 4, 5, 6} elements.

C = {p: p is a prime number} is an infinite set.Equivalent Sets

Equivalent sets are those which have an equal number of elements irrespective of what the elements are. Examples:

A = {1, 2, 3, 4, 5} and B = {x : x is a vowel letter} are equivalent sets because both these sets have 5 elements each.

S = {12, 22, 32, 42, …} and T = {y : y2 ϵ Natural number} are also equal sets.

Singleton Set

These are those sets that have only a single element. Examples:

E = {x : x ϵ N and x3 = 27} is a singleton set with a single element {3}

W = {v: v is a vowel letter and v is the first alphabet of English} is also a singleton set with just one element {a}.

Universal Set

A universal set contains ALL the elements of a problem under consideration. It is generally represented by the letter U. Example:

The set of Real Numbers is a universal set for ALL natural, whole, odd, even, rational and irrational numbers.

D = {k: k is a real number} is also an infinite set.

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