Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.- If there exists a function
such that
, then
is surjective
Let us start by the first implication.
Our hypothesis is that the function
is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets
. Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set
choose only one element
, and notice that
.
So, we can define the function
as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function
such that
.
Take an element
, then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element
we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.
Answer: p + 5 = new amount
Step-by-step explanation:
You have to write it the way it's read
she has p = current coins
she found 5 more, ( +5 )
write that down and you get p + 5 = new amount
hope this helps
plz mark brainleist
Hello!

Use the slope formula to solve for the slope of the line (m):

We can plug in the points (0, 4) and (1, 1) to solve:

Therefore, the slope of the line is -3.
20 cans in kilograms = 336 grams * 20 cans / 1000 = 6.72 kg
4n+15=70+n
I'm pretty sure this is the answer
Have a good day!