# Negation statement

#### 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?

#### 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.

#### relyt

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

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving