Question

How to negate this sentence: "The integer n is odd only if 3n is odd." Please help

Answer 1

@tkhunny

Answer 2

My all-time favorite way?

Just put "It is not the case that" in front of it.

Answer 3

I am not allowed to use "NOT" in my result.

Answer 4

@tkhunny

Answer 5

Well, why didn't you say so?

Do you have DeMorgan?

Answer 6

Yes, I have it,

Answer 7

and my result doesn't make sense to me
Let p: n is odd
q : 3n is odd
I have the given sentence is p--> q = ~p v q
now negate it, I have ~(~p vq) = p and ~q
which is " n is odd and 3n is even"
But it seems not good.

Answer 8

In this case, since odd and even are complete and mutually exclusive, you can negate "is odd" with "is even".

(p --> q)'
By DeMorgan = q' --> p'
Back to English = 3n is even only if n is even.

Answer 9

I wouldn't try that with blue and red. Blue is not the negation of red. There are other colors. :-)

Answer 10

can we do it this way?
assume n is even imply 3n is even

Answer 11

p'--->q'
if this is true then p--->q is false
does this sound good! not sure about this since i forgot my
essentials hehe

Answer 12

hehehe... I appreciate any help. I try to solve it algebraically but I failed.

Answer 13

n is even then n=2k
3n=3(2k)=2(3k) so even
this way?

Answer 14

What is your negation?

Answer 15

from this we got n is even implies 3n is even
the contradiction is true. then the statement is false!
i don't feel this is good lol! i really got rusty xD

Answer 16

heehe, we don't prove it is true or false, we just negate it.

Answer 17

if it is false means it is not valid! no? isn't that what negate mean?
first time i hear the word by the way lol

Answer 18

haahaha... negate means.... "make a research" !!

Answer 19

hmmm! are you sure? haha