Question

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

Answer 1

Odd numbers have a special property that when multiplied by any odd number, the product will always be odd. (The only exceptions are for different bases and modulus.) Examples include 3*5=15 35*3=105 127*325=41275

Answer 2

If I let p: 3n is odd
q : n is odd
then I have p--> q
negate it, ~(p--> q) = ~(~p and q) = p or ~q, right?
apply to the sentence I get 3n is odd or n is even.
but it sounds not good at all

Answer 3

thats not same as the given statement

Answer 4

if 3n is odd , then the integer n is odd

Answer 5

I think "only if" means a double implication.

Answer 6

Meaning p=>q and q=>p.

Answer 7

wait no , sorry

Answer 8

I need algebraic form,

Answer 9

Where there answer choices????

Answer 10

@math&ing001 it's just "only if". Is it the same meaning as "if and only if"??

Answer 11

@SCARLET_SPIDER no choices. :)

Answer 12

You cant negate it because it is true

Answer 13

Did anyone try Google

Answer 14

@swagmaster47 this is LOGIC, no matter what it is true or not, we can negate hihihi

Answer 15

Good luck.

Answer 16

@Loser66 you made a mistake there, p=>q means (not p or q)
So the negation would be not(not p or q) = p and (not q)

Answer 17

iff = (p & q) V (~p & ~q)
lol -_-

Answer 18

it cannot be a double implication, for example :

I'll go to movie `only if` you come with me

above statement doesn't conflict with below :
if you come with me ill go to hell

Answer 19

@math&ing001 thanks for pointing it out. You are right.

Answer 20

so change iff into two statment ,im sorry i dnt even know what im saying

Answer 21

whats ur logic @rational ?!
if you come with me ill go to hell
hehe and if i dint come you wont go to hell,
however iff is acomination of two statments :o

Answer 22

wait lol its only if , not iff -_-

Answer 23

nono, If you come with me, I won't go the the hell, I go to the heaven. hehehe

Answer 24

going to movie requires you
but if you come with me, we can go anywhere, it need not be just a movie :P

Answer 25

ill go anywhere , even to hell if its with u ;)

Answer 26

however i dint note the question is only if, i read it for some reason iff

Answer 27

so its just a single implication

Answer 28

I got it from here http://math.hws.edu/~mitchell/Math135F13/Equivalences.pdf
De Morgan law (part 3) , section (4)
so that I have to let p: n is odd
q : 3n is odd.
backward from mine. hehehe

Answer 29

im sry -_-
cant follow anything

Answer 30

hahaha... you are soooo cute.

Answer 31

ok use even instead of not odd

Answer 32

so
if n is not odd then 3n is not odd
will be

if n is even then 3n is even
if 3n is even, then n is even

Answer 33

@rational
Let do some algebra here
p: the integer n is odd
q: the integer 3n is odd
As the handout says, we have: p--> q = ~p v q

now negate it, we get p and ~q , which is the integer n is odd AND 3n is even

Answer 34

your logic is not good at: p --> q is not equivalent to ~p--> ~q

Answer 35

i was using contrapositive

Answer 36

not q goes to not p

Answer 37

"The integer n is odd only if 3n is odd." is same as : if n is not odd then 3n is not odd
p --> q is same as ~p --> ~q
This logic is wrong.

Answer 38

reread the problem please.

Answer 39

rash is right

Answer 40

see where is if statment

Answer 41

The given statement: "The integer n is odd only if 3n is odd"

Answer 42

i cant open my eyes any more , bbye.

Answer 43

@BSwan good night, girl

Answer 44

I don't think so. They are not equivalent!! A=> B is not equivalent to B=>A

Answer 45

you said "The integer n is odd only if 3n is odd." is same as : if n is not odd then 3n is not odd
so what does "is same as" mean??

Answer 46

he only say that
The integer n is odd only if 3n is odd.
B=3n is odd
A=The integer n is odd

the whole statment B-->A

Answer 47

ha!! that's backward from the handout I attached

Answer 48

the same as
only if 3n is odd then The integer n is odd

Answer 49

so go from here.

Answer 50

Give me your final sentence, pleeeease.

Answer 51

lets try this

p: I go to movie
q: if you come with me

"I go to movie only if you come with me."

is same as :
if you did not come with me, then i did not go to movie (~q => ~p)

is same as :
if I go to movie, then you did come with me (p=>q)

Answer 52

Yes, this logic is good.

Answer 53

does that looks okay ?

Answer 54

I was wrong initially -.- you're right :)

p: the integer n is odd
q: the integer 3n is odd

"The integer n is odd only if 3n is odd."

is same as :
if 3n is not odd then n is not odd (~q => ~p)

is same as :
if n is odd, then 3n is odd (p=>q)

Answer 55

let me delete my nonsense replies above

Answer 56

the negation of implication is simply ~p => ~q
right ?

Answer 57

I am not sure, that's why I make question here. hihi

Answer 58

The negation of an implication is the one I put above :
not (p=>q) = p and (not q)
In our case it would be : 3n is odd and n is even.