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I'm not sure what exactly you're asking about, but if you're asking about the difference between relations and functions, here's the answer.
In a relation, a value in the domain may have one or more values in the range. That is, for every x on graph there may be more than one value of y. In terms of word problems and such, x is the independent variable (i.e. time) and y is the dependent variable (i.e. temperature). Basically, if you graph a relation, you can draw a vertical line anywhere on the graph and that line may intersect one or more points on the graph. A circle or a horizontal parabola is a relation, not a function.
In a function, for every value in the domain there is only one value in the range. That is, for every value of x there is one and only one value of y. If you draw a vertical line anywhere on the graph of the function, it will only intersect the graph once. If it intersects the graph more than once, then that graph is not a function. An example of a function would be a vertical parabola, a line, or a cubic.
Hope that helps.
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Why all functions relation?
Function is a special case of relation. It means function is a relation but all relations are not functions. Therefore all functions are relations.
Is a function is always a relation?
Yes. Functions are always relations, but relations are not always functions.
What is the total number of reflexive and symmetric relations on a set containing n elements?
the total no of reflexive relation on an n- element set is 2^(n^2-n).
How do you Derive The Number of symetric relation of a Set 's' having n elements?
2^(n^2+n)/2 is the number of symmetric relations on a set of n elements.
How do you Derive The Number of reflexive relation of a Set 's' having n elements?
make a table as I did below for the set {a,b,c} with 3 elements. A table with all n elements will represent all the possible relations on that set of n elements. We can use the table to find all types of relations, transitive, symmetric etc. | a | b | c | --+---+---+---+ a | * | | | b | | * | | c | | | * | The total number of relations is 2^(n^2) because for each a or b we can include or not include it so there are 2 possibilities and there are n^2 elements so 2^(n^2) total relations. A relation is reflexive if contains all pairs of the form {x,x) for any x in the set. So this is the diagonal of your box. THESE ARE FIXED! No, in reflexive relation we still can decide to include or not include any of the other elements. So we have n diagonal elements that are fixed and we subtract that from n^2 so we have 2^(n^2-n) If you do the same thing for symmetric relations you will get 2^(n(n+1)/2). We get this by picking all the squares on the diagonal and all the ones above it too.
Why all functions relation?
Function is a special case of relation. It means function is a relation but all relations are not functions. Therefore all functions are relations.
Is a function is always a relation?
Yes. Functions are always relations, but relations are not always functions.
Is relationship a function?
I assume you mean a "relation". All functions are relations, but not all relations are functions.
What is true regarding functions and relation?
All functions are relations but all relations are not functions.
What is a relation and its inverse relation whenever both relations are functions?
inverse function
Can a function be a relation?
Functions are special types of relations.
When do you say that a given function is velation?
I assume you mean "relation". By definition, all functions are relations; but only some relations are functions.
Is any function a relation?
Yes. All functions are relations, but not all relations are functions. Functions have to have only one y-value per x-value.
Can you have a relation that is not a function?
Yes. The set of functions is a subset of the set of relations.
Can you have a function that's not a relation?
Yes. The set of functions is a subset of the set of relations.
What is the difference between relations and functions?
A function is a relation whose mapping is a bijection.
Are all relation are function?
Yes, but all relations are not functions.
