# Statement logic, negation

1. Jan 28, 2009

### test_notagain

1. Negate the following statements

(i): $$\forall$$x$$\in$$R $$\exists$$y$$\in$$R such that x+y=0

(ii): introduction: Each of us got, let's say, 20 bags of green apples.
Actual Statement: At least one of us (each) found at least one red apple in at least one bag (each). (Each person and each one of it's bags are treated separately)

2. Relevant equations/3. The attempt at a solution
No idea. I'm completely lost here.

Please help, as I have no idea how to negate complex/multi-element statements.

2. Jan 28, 2009

### tiny-tim

Welcome to PF!

Hi test_notagain! Welcome to PF!

(have an exists: ∃ and an in: ε and a for-all: ∀ )

Let's try (ii) first …

the opposite of something beginning "At least one of us has …" is "There exists one of us who hasn't …"

can you go on from there?

3. Jan 29, 2009

### test_notagain

Re: Welcome to PF!

Thanx tiny-tim, but I still don't get it cuz there are 3 parts to statement (ii)... And what is the negation of the first one (i)?

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