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Chapter 1: Problem 89

Determine whether the statement is true or false. Justify your answer. Every relation is a function.

Short Answer

Expert verified
The statement 'Every relation is a function' is false. A function is a specific type of relation where every element in the domain is related to exactly one element in the co-domain. However, a relation doesn't require this uniqueness, and an element in the domain can be associated with more than one element in the co-domain.

Step by step solution

01

Understanding the terms

Firstly, it is important to understand the terms relation and function in mathematical context. A relation in mathematics can be defined as a set of ordered pairs. On the other hand, a function is a special relation where each input has exactly one output. In other words, every element in the domain (set of inputs) is related to exactly one element in the co-domain (set of outputs).
02

Analyzing the given statement

The given statement is 'Every relation is a function'. This means, according to the statement, every set of ordered pairs (relation) has the unique property that each input corresponds to exactly one output. But, we know that it is not necessary for a relation, as in case of a relation an element from the domain can be associated with more than one element in co-domain.
03

Conclusion

From our analysis in step 2 it's clear, not every relation can be considered a function because not every set of ordered pairs follows the unique property that each element in the domain is related to exactly one element in the co-domain. Hence, it can be concluded that the given statement is false.

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