Explain why the following statement is false: If ordered pairs form a function,then the number of x-values are less than the number of ordered pairs.
For a function y = f(x) defined by ordered pairs (x, y), for each value of x the value of y = f(x) has to be unique. It is not possible for a value of x to give two values of y = f(x) as it would then not be possible to decide which of the two values of y should be chosen for the value of x.
It should be kept in mind that there is no restriction on the number of values for x that give the same value of y when y = f(x) is applied but it is essential that no two values of x give the same value for y.
This is the reason why the statement "If ordered pairs form a function,then the number of x-values are less than the number of ordered pairs." is false.
I think the statement is false because the definition of a functions says that every x must have a unique y. If the number of x values is less than the number of ordered pairs, then two x values must share a y value, and the set of ordered pairs would not be a function.