a Does the set represent a function Explain b Is this relati

a. Does the set represent a function? Explain.

b. Is this relation onto? If yes, give a proof; otherwise, give a counterexample.

c. Is this relation 1-1? If yes, give a proof; otherwise, give a counterexample.

Please fully answer all parts of the question (a, b, and c). Thank you.

Solution

a. It is not a function because a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. In the given question 4 is used with many inputs.hence, not a function.

b. It is a onto funtion because  a function f from a set X to a set Y is surjective (or onto), or a surjection, if every element y in Y has a corresponding element x in X such that f(x) = y. The function f may map more than one element of X to the same element of Y. In the given question all the elements from one set is mapped with a corresponding element.

c.It is one one to one because A function f from A to B is called one-to-one (or 1-1) if whenever
f (a) = f (b) then a = b.   No element of B is the image of more than one element in A. in the given question 4 has many images.