Question

Negate this sentence: "The integer n is odd only if 3n is odd"
I need method to get the answer, not the answer itself
Please, help

Answer 1

@perl

Answer 2

The integer n is odd only if 3n is even ??

Answer 3

How to get it?

Answer 4

p only if q means ' if p then q '

Answer 5

This is what I did:
p: the integer n is odd
q: 3n is odd
p--> q
then negate it

Answer 6

write it as an "if ... then..." statement first, then you will unconfuse yourself

Answer 7

I am not sure if it is right or not..

It is what I think..

Answer 8

how do we negate ' if p then q ' ?
the negation is p and (not q)

Answer 9

the "only if" is annoying and confusing
change it to "if P then Q" and you can negate it easily

Answer 10

p--> = ~p or q

Answer 11

negate the right hand side to gate p and not q

Answer 12

but it 's weird when verbalizing it.

Answer 13

If 3n is odd, then integer n is odd...

Answer 14

Let p = n is odd
q = 3n is odd

the original statement is 'if n is odd then 3n is odd. '
The negation is ' n is odd and 3n is not odd '

Answer 15

so the negation is n is odd and 3n is even

Answer 16

I am not allowed to use "Not" in my sentence

Answer 17

"not odd' we call "even" on planet earth

Answer 18

the opposite of odd (for integers) is even . if n is not odd, then n is even

Answer 19

@perl so that what I got, but it is weird, right? how n is odd and 3n is even, hahaha??

Answer 20

and we are assuming we are talking about ingegers

Answer 21

loser, yes it is weird, because it is false . (the original statement is true)

Answer 22

if you negate a true statement, you will get a false statement.

Answer 23

this is just a logical exercise ;)

Answer 24

if a statement is true, then its negated form will be false

Answer 25

ooooohhh.... yessssssssssss!

Answer 26

Thank you everybody. :)

Answer 27

lets prove the original statement is true.
Given integer n is odd, then by definition of odd integer
n = 2k+1 for some integer k.
But now 3n = 3(2k+1)
And
3n =3(2k+1)
= 6k + 3
= 6k + 2 + 1 = 2(3k+1) + 1
So we have 3n = 2*m + 1 , where m = 3k+1
so 3n is an odd number by definition of odd integer.

Answer 28

its good to practice these proofs on your own

Answer 29

and since this is a true statement (since we proved it), if you negate it you know it will be false

Answer 30

I have proving problems like this too. It's not too hard to go over. But this problem confused me and your statement " negate true will get a false one" enlightens me. Thanks again.