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Chapter 1: Problem 115

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.

Step by step solution

01

Understanding the concept of a relation

A relation from a set \(X\) to a set \(Y\) is simply a set of ordered pairs, where the first element of each pair belongs to \(X\) and the second element belongs to \(Y\).
02

Understanding the concept of a function

A Function from a set \(X\) to a set \(Y\) is a type of relation where each element from set \(X\) is related to exactly one element in set \(Y\). This means a function will never assign to the same input two or more different outputs, i.e., there should be a unique relation for each input.
03

Analyzing the relation-function relationship

As per the definitions of a relation and a function, it is clear that while every function is a relation (as it pairs elements from one set to another), not every relation is a function (as there may be more than one output for a single input in a relation).

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Most popular questions from this chapter

Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) \(y\) varies inversely as \(x .(y=3\) when \(x=25\).

Determine whether the function has an inverse function. If it does, find the inverse function. $$ g(x)=\frac{x}{8} $$

Find a mathematical model for the verbal statement. For a constant temperature, the pressure \(P\) of a gas is inversely proportional to the volume \(V\) of the gas.

Use the given value of \(k\) to complete the table for the inverse variation model $$y=\frac{k}{x^{2}}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=\frac{k}{x^{2}} & & & & & \\ \hline \end{array}$$ $$ k=10 $$

Use the given value of \(k\) to complete the table for the direct variation model $$y=k x^{2}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=2 $$
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