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
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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