Question

which sets are commonly known as infinite set.hhhhjjo



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Answer 1

the sets in which numbers do not end

the process by which green plants and some other organisms use sunlight to synthesize nutrients from carbon dioxide and water.

Answer 2

Finite and infinite sets are two of the different types of sets. The word ‘Finite’ itself describes that it is countable and the word ‘Infinite’ means it is not finite or uncountable. Here, you will learn about finite and infinite sets, their definition, properties and other details of these two types of sets along with various examples and questions.

Definition of Finite set

Finite sets are the sets having a finite/countable number of members. Finite sets are also known as countable sets as they can be counted. The process will run out of elements to list if the elements of this set have a finite number of members.

Examples of finite sets:

P = { 0, 3, 6, 9, …, 99}

Q = { a : a is an integer, 1 < a < 10}

A set of all English Alphabets (because it is countable).

Another example of a Finite set:

A set of months in a year.

M = {January, February, March, April, May, June, July, August, September, October, November, December}

n (M) = 12

It is a finite set because the number of elements is countable.

Cardinality of Finite Set

If ‘a’ represents the number of elements of set A, then the cardinality of a finite set is n(A) = a.

So, the Cardinality of the set A of all English Alphabets is 26, because the number of elements (alphabets) is 26.

Hence, n (A) = 26.

Similarly, for a set containing the months in a year will have a cardinality of 12.

So, this way we can list all the elements of any finite set and list them in the curly braces or in Roster form.

Properties of Finite sets

The following finite set conditions are always finite.

A subset of Finite set

The union of two finite sets

The power set of a finite set

Few Examples:

P = {1, 2, 3, 4}

Q = {2, 4, 6, 8}

R = {2, 3)

Here, all the P, Q, R are the finite sets because the elements are finite and countable.

R ⊂ P, i.e R is a Subset of P because all the elements of set R are present in P. So, the subset of a finite set is always finite.

P U Q is { 1, 2, 3, 4, 6, 8}, so the union of two sets is also finite.

The number of elements of a power set = 2n.

The number of elements of the power set of set P is 24 = 16, as the number of elements of set P is 4. So it shows that the power set of a finite set is finite.

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Answer By shreyas