negation

[Lvanalstyne]

I am having trouble with some negation problems. I have researched the internet and looked through a couple of math books, however the information is weak. This seems simple enough, but I just want to make sure I am doing it correctly. Any help would be appreciated.

a < b -----the negation I think would be a is greater than or equal to b
n is an integer and n > 5 would be n is not an integer and n <= 5
a < b < c- again I believe this would run on track with the first answer which is a >=b>=c

now they ask to write negation of -----The product of any two rational numbers is always rations- I am not sure how to attack this one and I want to make sure I am on the right track... Thanks for any help you can give...........

 

[daon2]

I am having trouble with some negation problems. I have researched the internet and looked through a couple of math books, however the information is weak. This seems simple enough, but I just want to make sure I am doing it correctly. Any help would be appreciated.

a < b -----the negation I think would be a is greater than or equal to b

Right. When is a not less than b? When a is at least b.

n is an integer and n > 5 would be n is not an integer and n <= 5

a < b < c- again I believe this would run on track with the first answer which is a >=b>=c

These are not right. Think about what makes the statement false. The first is false if either n is not an integer or if n is at most 5. The point here is the negation of an "and" is an "or."

The second statement can be rewritten as a <b and b<c. Try it now.

now they ask to write negation of -----The product of any two rational numbers is always rations- I am not sure how to attack this one and I want to make sure I am on the right track... Thanks for any help you can give...........

This can be rewritten as an implication: If a and b are rational numbers then a*b is rational. Do you know how to negate an implication?