George Washington was the first president of USA.
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.
737 people I’m pretty sure
Answer:
d
Step-by-step explanation:

<h3>area of shaded figure= </h3>
<h2>area of whole rectangle</h2>
= lengthx breadth=15x30= 450 cm²
<h3>area of unshaded region= lengthx breadth= (30-8)x 15cm²= 22x 15cm²= 330cm²</h3>
<h3>are of shaded region</h3>
= area of whole rectangle -area of unshaded region= 450cm²-330cm²= 120cm²
therefore 120 is correct answer