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3 years ago

What is y after the following statement is executed? x = 0; y = (x > 0) ? 10 : -10;?

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

4 0

Ahh, i can see youre doing some programming. In C++ this output is -10
So -10

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DIscrete Math

Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

3 0

3 years ago

Can someone help me fast pls

kykrilka [37]

Your answer would be C.) 18oz

5 0

3 years ago

Tickets for the school concert were 3$ and 2$. If 245 tickets were sold for a total of $630, how much of each kind were sold?

Hatshy [7]

2x + 3y = 630
x + y = 245 then you want to get rid of x so in the second equation × by -2 and get -2x -2y =-490 subtract this equation from the first to get y=$140 substitute 140 in for y and get x= $105 and 2x=210 and 3y=420 210 +420=630

7 0

3 years ago

Solve 2a 2 - 3a - 2 = 0<br><br> {-1/2, 2}<br> {1/2, -2}<br> {}

d1i1m1o1n [39]

Apply slip and slide
a^2-3a-4
(a-4)(a+1)
(a-2)(2a+1)

Find zeros
a-2=0
a=2

2a+1=0
2a=-1
a=-1/2

Final answer: {-1/2, 2}

8 0

3 years ago

Read 2 more answers

The band is selling boxes of fruit to raise money for new uniforms. Boxes of oranges cost $12 per box and boxes of grapefruits c

ValentinkaMS [17]

Answer:

The band is selling boxes of fruit to raise money for new uniforms. Boxes of oranges cost $12 per box and boxes of grapefruits cost $15 per box. To get free shipping on all of the fruit each band member must sell at least 25 boxes of fruit. In order to meet your goal, you want to sell at least $500 worth of fruit.

6 0

2 years ago