Solve Predicate Logic Homework Equations

.~!@#
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Homework Statement



1) (∀xεℝ)((x≠0)→((∃yεℝ)(xy=1)

2) (∃yεℝ)(∀xεℝ)((x≠0)→(xy=1))



Homework Equations



∃ - there exists
∀ - for all
→ implication

The Attempt at a Solution



The brackets and implication are throwing me for a loop

1) for all real numbers, there exist another real number such that their product is 1. TRUE

2) There exists a real number y, such that any real number and y will have a product of 1. False.

?
 
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.~!@# said:

Homework Statement



1) (∀xεℝ)((x≠0)→((∃yεℝ)(xy=1)

2) (∃yεℝ)(∀xεℝ)((x≠0)→(xy=1))

Homework Equations



∃ - there exists
∀ - for all
→ implication

The Attempt at a Solution



The brackets and implication are throwing me for a loop

1) for all real numbers, there exist another real number such that their product is 1. TRUE

2) There exists a real number y, such that any real number and y will have a product of 1. False.

?
Hello .~!@# !

What's the question?

Do you want to know if your answers are correct, or do you want your translation into English checked ? ... or what??
 
both
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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