If X is a set containing n elements:

Mathematics

1 answer:

Hatshy [7]4 years ago

7 0

<h2>Answer:</h2>

Ques 1)

Number of functions from X to X are: $n^n$

Ques 2)

Number of relation from X to X are: $2^{n^2}$

<h2>Step-by-step explanation:</h2>

Relation--

A relation from a set A to set B is the set of all the ordered of the type:

(a,b) where a belongs to A and b belongs to B.

if A has m elements and B has n elements.

Then the total number of relation from A to B are: $2^mn$

Function--

A function from a set A to set B is the set of all the ordered pair where each element of set A is mapped to a single element of the other set.

i.e. every element has a single image.

if A has m elements and B has n elements.

Then the total number of functions from A to B are: $n^m$

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fiasKO [112]

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Hope this helps mate

8 0

4 years ago

Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$