# Negation statement

1. Mar 1, 2009

### relyt

Statement:

($$\exists_{x} \in$$ R) ($$\forall_{y} \in$$ R) (3x + 2y = 7)

Trying to find negation statement. This is what I think it is:

($$\forall_{x} \in$$ R)($$\exists_{y} \in$$ R) (3x + 2y ≠ 7)

Is this close?

2. Mar 1, 2009

### phreak

I'm having trouble reading this notation, but I'm assuming the first statement says "There exists an x in R such that for all y in R, 3x + 2y = 7."

To make this backwards, we would need to say, "For each x in R, there exists a y in R such that 3x + 2y does not equal 7," so if I have interpreted your notation correctly, I think your answer is correct.

3. Mar 1, 2009

### relyt

Thanks, phreak. Yes, that is how it should read.