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Determine whether the following chim is alays true Or whether I can be false in some cases. Justify your answerThe expression Vxez(xty = xy) is a proposition (rathe...

Question

Determine whether the following chim is alays true Or whether I can be false in some cases. Justify your answerThe expression Vxez(xty = xy) is a proposition (rather than merely a predicate).

Determine whether the following chim is alays true Or whether I can be false in some cases. Justify your answer The expression Vxez(xty = xy) is a proposition (rather than merely a predicate).



Answers

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If $x<y,$ then $e^{x}<e^{y}$.

For this problem, you're to determine if the statement is true or false. Now it says that if Y is equal to erase the X over X square, then why prime is equal to erase two X over two X. Now by quotient rule the derivative of Y is white brand. That's equal to x squared times the derivative of the numerator, E to the X minus each of the X times the derivative of the denominator X squared over the square of X squared. And so we get X squared times E race to x minus, erase the X times two X Over X to the 4th power. And if we factor out XC race X, We have x times erase two x. These times X minus to all over X to the 4th power. Or You have erased x times X -2 over X cubed. And since this is not equal to erased X over two X. Then we say that the statement is false.

In this problem, we have the first statement given to us as X plus Y equals two. Y plus X is true for every real number X and Y. The negation of this is that there exists, it exists real numbers X and Y such stock, or for which X plus Y is not equal to Y. Plys X. This is not the same as statement, too, but says that there exist real number X and Y. For which exploits were equals two Y plus six. Does the given statements are not the negation of each other? Not negation. Uh huh. Egypt. That's all.

In this problem, we want to determine whether or not the following statement is true or false, but the function Z is equal to eat the X. Y and Z squared DZ dy dx is X Y plus one times E V Xy This question is testing our understanding of multi variant differentiation. In order to solve, we must understand that defined possibilities. We use single variable differentiation techniques differentiated with respect to the different gene variable treating other variables is constant along the way. The example here now outlined an origin showcases the start for the function X. Y. So just do what we want to do is to solve for the given partial derivatives. Note that it doesn't matter if we differentiate directed YR experts because there's a rule for partial derivatives that D squared dx DY is equal to D squared dy dx. So in that case we'll go with X O d d d d d d x is X Y, two MG X, X Y. Or Y E X Y. Or the chain rule an exponential, Thus D squared dx Dy DZ DY Y e x Y. Which is easy, X Y plus Y E x Y acts by the chain rule and products will, or one plus X, Y e x Y. Thus d squares E d x Y equals X Y plus one of the X Y and R statement is true.

In this problem we need to determine whether a given statement is true or false. Now the given statement is that if X and Y are both negative, then the models of Express White is equal to the models of Express. The models of White. Now, in order to determine whether or not this is true or false. First of all, that is considered to real numbers X and Y. Which are both negative, so they are both president zero. Now the models of X will be equal to minus X. And sex is less than zero. Similar. Listens why is less than zero? So the models of Y would be equal to minus wife. Now if we consider the modelers of X. Plus White and note that since X is negative and why is also negative. So Express White will be negative. So the value of the models of Express White will be equal to minus of Express White. This is because explode, Swine is less than C. So if we consider the given statement we have, the models of Express White is equal to models of extras models of white. So if we consider the models of Express White Over here, we have seen this is equal to minus of Express White. So we can write that as minus six minus white, or rather minus X. Plus minus White, minus X. Is equal to the models of X and minus Y. Is equal to the modelers of white. So we can write this as the models of X plus the models of white. Hence we can see that the models of experts. Y is equal to the models of X plus the models of white. And hence the given statement is true.


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