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lgbasallote
Group Title
Prove that if n is an integer then 3n + 2 is even, then n is even
 2 years ago
 2 years ago
lgbasallote Group Title
Prove that if n is an integer then 3n + 2 is even, then n is even
 2 years ago
 2 years ago

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mathslover Group TitleBest ResponseYou've already chosen the best response.0
we have to prove two things? : 1) 3n+2 is even , 2) n is even
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
no, it's prove n is even GIVEN 3n + 2 is even.
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
ok , thanks
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
If 3n + 2 is even, then 3n is even
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
if 3n is even then n is even.
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.3
Given : 3n+2 is even To prove : n is even 3n+2 = 2k 3n = 2k2 3n = 2(k1)
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
not true for n=1 ? 3+2=5<not even
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
@hartnn GIVEN that 3+2 is even, n is even
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
IF 3n+2 is even , prove that is even. @hartnn
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
But it's not so no guarentee is made.
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
lets clear it from @lgbasallote what the exact question is...
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
@lgbasallote ?
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
Just out of interest whats the general way to prove something is even, divide by 2?
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.3
if we prove a number is of form 2k that proves it is even
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
right I see
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
btw any1 here mind taking a look at my question? http://openstudy.com/updates/5078b9d7e4b02f109be44f95
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
sorry i just came back....anyway...i'd llike to see how proving by contradiction is done.. direct proof is too easy
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
but whats the question ?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
the statement in the blue box
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
forgot to mention by the way....that the direct proof done here was wrong
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
they took n as the condition... 3n + 2 is supposed to be the condition
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
so 3n + 2 = (a different n)?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
if 3n+2 is even , n is even. thats the question and u need to prove that using contradiction, right ?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
if you use direct proof... it should be 3n + 2 = 2x then prove n is even
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
but like i said...should be contradiction though
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
well okay thats easy enough, too
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
hmmm then let's see you try
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
All you have to say is that assume that given 3n + 2 is even, n is not even Then n has to be odd. Thus, 3n + 2 can be represented as 2k + 1 for some k
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.3
Given : 3n+2 is even To prove : n is even to prove by contradiction, lets assume the opposite  lets assume n is odd, 3n+2 = 2k 3n = 2k2 3n = 2(k1) so we got the right side as even number, but we assumed n is odd, so left 3n becomes odd  contradiction
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
@sara12345 you cannot say "assume that n is odd" and then equate it to 2k
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
@sara12345 how is that contradiction
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.3
we do that always in proof by contradiction
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.3
RHS = even , LHS = odd => contradiction
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
i was referring to your solution
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
How can you prove that it equals 2k, though?
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
if 3n + 2 is odd, then it can be expressed 3n + 2 = 2k + 1. solving for n gives \[n = \frac{2k}{3}  1\] substituting back for n gives \[3 (\times \frac{2k}{3}  1) + 2 = 2k + 1so\] so \[2k  1 = 2k + 1 \] which is absurd
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
hmm seems legit
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
so in proof by contradiction...you still substitute back huh
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
As @JamesWolf showed for you,
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
you take the contradiction, show that it is not internally consistent, and therefore it cannot be true.
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
no its not legit
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
ive been an idiot int he first step
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
@JamesWolf no, you inadvertently put up my proof.
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.3
in proof by contradiction, we assum e the opposite of what we need to prove as true, and proceed, not the opposite of given conditions
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
if you assume n is odd and 3n + 2 is even... 3(2k + 1) + 2 6k + 3 + 2 6k + 2 + 3 2(3k + 1) + 3 so even + odd would be odd...so contradiction i suppose that works as well
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
@sara12345 yes you're right, sorry.
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
yes its right actually i managed to not divide by 3 at the start, but luckily i messed up by not multiplying  1by 3 at the end
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
oh so you take the negation of q then proceed from there?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
anyway...is my proof right?
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.3
lgba ur proof is more correct as it shows the assumption n is odd as well by letting n =2k+1
 2 years ago
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