In fact, every function is a relation. However, not every relation is a function. A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y.

That is, given an element x in X, there is only one element in Y that x is related to.

For example, consider the following sets X and Y. Let me give you a relation between them that is not a function;

X = { 1, 2, 3 }

Y = { a , b , c, d }

Relation from X to Y : { (1,a) , (2, b) , (2, c) , (3, d) }

This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c

Relation from X to Y that is a function: { (1,d) , (2,d) , (3, a) }

This is a function since each element from X is related to only one element in Y. Note that it is okay for two different elements in X to be related to the same element in Y. It's still a function, it's just not a one-to-one function.

So, we can say that function is a type of relation.

Which means whatever a function occurs, it will be a relation from one set to other.

But when a relation occurs it may be a function but need not be always a function.

Hence, a function is always a relation but relation is not always a function.

8 0

3 years ago

If y varies directly as x^2 and y=12 when x=2, find y when x=5

Shkiper50 [21]

$y=ax^2\\\\y=12\ \ \ and\ \ \ x=2\ \ \ \Rightarrow\ \ \ 12=a\cdot 2^2\ \ \ \Rightarrow\ \ \ a= \frac{4}{12}= \frac{1}{3} \\\\y=\frac{1}{3} x^2\\\\x=5\ \ \ \Rightarrow\ \ \ y=\frac{1}{3} \cdot5^2=\frac{25}{3} =8\frac{1}{3}$

7 0

3 years ago

If 2/3 of the girls have brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class have neither blue or

alex41 [277]

1/7th of girls have neither

4 0

3 years ago