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Chapter 1: Problem 116

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

Short Answer

Expert verified
The statement 'Every function is a relation' is true.

Step by step solution

01

Understanding definitions

In mathematics, a relation between two sets is defined as a set of ordered pairs containing one object from each set. A function, on the other hand, is a special type of relation. In a function, every element of the first set is related to exactly one element of the second set.
02

Analyzing the statement

The statement is 'Every function is a relation'. From the definitions, it's understood that every function is indeed a relation because it is a specific type of a relation, but not all relations are functions since a relation allows an element of the first set to be related to more than one element of the second set.
03

Final Verification

So, the statement 'Every function is a relation' is true based on the definitions of functions and relations in mathematics. This is because a function is simply a special case of a relation where each input element has exactly one associated output element.

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