Math, asked by raushanboss1234, 2 months ago

what are Cardinal number of a set​

Answers

Answered by sundar1718k
0

Answer:

Here, we formalize these relationships between sets and whole numbers.

Sets of Numbers: The set of natural numbers (or counting numbers) is the set N = {1, 2, 3, …}.

The set of whole numbers is the set W = {0, 1, 2, 3, …}.

Cardinal Number of a Set: The number of elements in a set is the cardinal number of that set.

Notation: If a set A is equivalent to the set {1, 2, 3, …, N}, we write n(A) = N and say “The cardinal number of set A is N.”

Also, n(Ø) = 0. The cardinal number for an empty set is zero.

Example: Let C = {#, $, %, &}. Show n(C) = 4.

# $ % &

| | | |

1 2 3 4

Hence, C is equivalent to {1, 2, 3, 4} and n(C) = 4 since a 1-1 correspondence can be setup between C and {1, 2, 3, 4}.

Example: For M = {red, blue, green, yellow, orange}, n(M) = 5.

The symbol “n(M) = 5” is read, “The cardinal number of set M is equal to 5.”

Take the time to set up a 1-1 correspondence between M and {1, 2, 3, 4, 5}.

Example: For T = {2, 4, 6, 8, 10, 12, 14, 16}, n(T) = 8.

On a sheet of paper, set up a 1-1 correspondence between T and {1, 2, 3, 4, 5, 6, 7, 8}.

Example: In this picture, the circles represent sets A and B. The dots inside are the elements of the sets. We need to make sure we look at an entire circle, even though the circles overlap.

Venn Diagram

n(A) = 5 n(B) = 8

Step-by-step explanation:

thankyou

Answered by Itzpureindian
0

Cardinal Number of a Set: The number of elements in a set is the cardinal number of that set. Notation: If a set A is equivalent to the set {1, 2, 3, …, N}, we write n(A) = N and say “The cardinal number of set A is N.” Also, n(Ø) = 0. The cardinal number for an empty set is zero.

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