Solve Predicate Logic Homework Equations

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The discussion centers on two predicate logic statements regarding real numbers and their products. The first statement asserts that for every non-zero real number, there exists another real number such that their product equals one, which is deemed true. The second statement claims that there exists a real number y such that any non-zero real number multiplied by y equals one, which is considered false. Participants seek clarification on whether their interpretations of the statements are correct and request assistance with the logical implications involved. The conversation highlights the complexities of understanding predicate logic and the importance of precise interpretation.
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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
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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