(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Alright here it is:

Theorem: if there exists an x belonging to reals such that (x^2)-x-2=(x^2)-4 then 1=2.

Remark: note that there is such an x belonging to reals.

Proof:

1) by hypothesis assume there exists an X belonging to reals such that (x^2)-x-2=(x^2)-4

2)factor each side,

3)resulting in (x-2)(x+1)=(x-2)(x+2)

4)divide each side by (x-2),

5)resulting in x+1=x+2

6)subtract x from each side, resulting in 1=2

1) What terminology (quantifiers, predicates) can be used to express the entire statements 1,3,5

2)Why is this proof fallacious, refer to statements by their numbers. Hint: What are the domains for each statement?

2. Relevant equations

3. The attempt at a solution

Ok, my attempt at part one (is

Theorem: ([tex]\exists[/tex]X [tex]\in[/tex][tex]\Re[/tex]) [tex]\right arrow[/tex] ((x^2)-x-2=(x^2)-4))

Statement 1: [tex]\exists[/tex]X [tex]\in[/tex][tex]\Re[/tex] ((x^2)-x-2=(x^2)-4))

Statement 3:[tex]\exists[/tex]X [tex]\in[/tex][tex]\Re[/tex](x-2)(x+1)=(x-2)(x+2)

Statement 5:[tex]\exists[/tex]X [tex]\in[/tex][tex]\Re[/tex]x+1=x+2

For part 2, i am quite lost, the problem is the use of existential quantifier. My guess is a division by zero somewhere, but otherwise, I need a bigger hint.

1. The problem statement, all variables and given/known data

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Discrete fallacious proof

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