# Math Definition: Inclusive & Exclusive

• hkhero
For example, the inclusive "or" of A and B is true if A is true, if B is true, or if both A and B are true. The exclusive "or" is only true if either A or B is true, but not both.
hkhero
What's the general math definition for inclusive and exclusive? Thanks fr everything and ty

hkhero said:
What's the general math definition for inclusive and exclusive? Thanks fr everything and ty

The "general" math definition is just the usual dictionary definition: "inclusive" means including everything under discussion and "exclusive" means excluding everything under discussion. Of course, what is under discussion depends upon the specific situation. In "the set of numbers between 0 and 1, inclusive" the word "inclusive" means that the endpoints, for which the word "between" is ambiguous, are included. In "the set of numbers between 0 and 1, exclusive" they are excluded.

Inclusive and exclusive are used in logic and set theory in the context of the"or" or "union" operation. Inclusive means either or both, while exclusive means either but not both.

## What is the difference between inclusive and exclusive in math?

Inclusive in math means that the starting and ending numbers are included in the set or range. For example, if we say "count from 1 to 10 inclusively," we would include the numbers 1 and 10 in the set. On the other hand, exclusive in math means that the starting and ending numbers are not included in the set or range. Using the same example, if we say "count from 1 to 10 exclusively," we would not include the numbers 1 and 10 in the set, but instead count from 2 to 9.

## How can you represent inclusive and exclusive in mathematical notation?

Inclusive can be represented using square brackets [ ] around the numbers, while exclusive can be represented using parentheses ( ) around the numbers. For example, the inclusive set of numbers from 1 to 10 would be written as [1, 10], while the exclusive set would be written as (1, 10).

## When do we use inclusive and exclusive in math?

Inclusive and exclusive are used in different mathematical operations and concepts. For example, when defining a range of numbers, we may use inclusive or exclusive notation to specify whether the starting and ending numbers are included or not. In probability and statistics, inclusive and exclusive are used to define the boundaries of events or outcomes. In set theory, inclusive and exclusive are used to specify the elements in a set.

## What is an example of using inclusive and exclusive in a real-life scenario?

An example of using inclusive and exclusive in a real-life scenario is when determining the age range for a children's movie. If the movie is appropriate for children aged 5 to 10 inclusively, then children who are 5 or 10 years old can watch the movie. However, if the movie is only appropriate for children aged 6 to 9 exclusively, then children who are 6 or 9 years old cannot watch the movie.

## What happens if we do not specify whether a range is inclusive or exclusive?

If we do not specify whether a range is inclusive or exclusive, it is assumed to be inclusive by default. This means that the starting and ending numbers are included in the range. It is important to specify whether a range is inclusive or exclusive to avoid confusion and ensure accuracy in mathematical calculations and interpretations.

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