If A = {a, b, c, d} and Y = {x, y, z}. And g's G(a) = y, G(b) = z, G(c) = x, G(d) = y. Is it 1 to 1 or onto

If A = {a, b, c, d} and Y = {x, y, z}. And g's defined as


G(a) = y, G(b) = z, G(c) = x, G(d) = y.


Is G one-to-one or Onto? Why or why not?

If A = {a, b, c, d} and Y = {x, y, z}. And g's G(a) = y, G(b) = z, G(c) = x, G(d) = y. Is it 1 to 1 or onto
First... is G a function? Onto and one-to-one only apply if G is a function.





Given: A = {a, b, c, d} and Y = {x, y, z}


G(a) = y, G(b) = z, G(c) = x and G(d) = y.





G is a function. A mapping of G from A to Y is called a function if for an element a in A and all elements in Y, whenever G(a) = y and G(a) = z, y = z. In this case, G(a) is mapped once to an element in Y. G(b) is mapped once to an element in Y. G(c) is mapped once to an element in Y and G(d) is mapped once to an element in Y. It is the same as saying each element a from A is mapped to only ONE element y in Y.





G is onto.


1. G is a function.


2. A function G from A to Y is called onto if for all elements a in A there is element a in A such that G(a) = y. The elements of Y are {x, y, z}. x is mapped from G(c). y is mapped from G(a). z is mapped from G(b). It is the same as saying all elements of Y are mapped from A. The elements x, y, and z in Y are all used.





G is not one-to-one.


1. G is a function.


2. A function G from A to Y is called one-to-one if whenever G(a) = G (b) then a = b. In this case, you've fot G(a) = y and G(d) = y. So G(a) = G(d). G would only be a one to one function from A to Y if a = d. But I'm assuming that a, b, c, and d are unique elements of A. It is the same as saying one-to-one means that every element in Y is mapped from only one element in A. In this case y is mapped from a and d, so it's not onto.