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Prove that if n is an integer then 3n + 2 is even, then n is even
 one year ago
 one year ago
Prove that if n is an integer then 3n + 2 is even, then n is even
 one year ago
 one year ago

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

vf321Best ResponseYou've already chosen the best response.1
no, it's prove n is even GIVEN 3n + 2 is even.
 one year ago

vf321Best ResponseYou've already chosen the best response.1
If 3n + 2 is even, then 3n is even
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
if 3n is even then n is even.
 one year ago

sara12345Best 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)
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
not true for n=1 ? 3+2=5<not even
 one year ago

vf321Best ResponseYou've already chosen the best response.1
@hartnn GIVEN that 3+2 is even, n is even
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
IF 3n+2 is even , prove that is even. @hartnn
 one year ago

vf321Best ResponseYou've already chosen the best response.1
But it's not so no guarentee is made.
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
lets clear it from @lgbasallote what the exact question is...
 one year ago

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

sara12345Best ResponseYou've already chosen the best response.3
if we prove a number is of form 2k that proves it is even
 one year ago

vf321Best ResponseYou've already chosen the best response.1
btw any1 here mind taking a look at my question? http://openstudy.com/updates/5078b9d7e4b02f109be44f95
 one year ago

lgbasalloteBest 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
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
but whats the question ?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
the statement in the blue box
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
forgot to mention by the way....that the direct proof done here was wrong
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
they took n as the condition... 3n + 2 is supposed to be the condition
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.0
so 3n + 2 = (a different n)?
 one year ago

hartnnBest 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 ?
 one year ago

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

lgbasalloteBest ResponseYou've already chosen the best response.1
but like i said...should be contradiction though
 one year ago

vf321Best ResponseYou've already chosen the best response.1
well okay thats easy enough, too
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
hmmm then let's see you try
 one year ago

vf321Best 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
 one year ago

sara12345Best 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
 one year ago

vf321Best ResponseYou've already chosen the best response.1
@sara12345 you cannot say "assume that n is odd" and then equate it to 2k
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
@sara12345 how is that contradiction
 one year ago

sara12345Best ResponseYou've already chosen the best response.3
we do that always in proof by contradiction
 one year ago

sara12345Best ResponseYou've already chosen the best response.3
RHS = even , LHS = odd => contradiction
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
i was referring to your solution
 one year ago

vf321Best ResponseYou've already chosen the best response.1
How can you prove that it equals 2k, though?
 one year ago

JamesWolfBest 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
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
so in proof by contradiction...you still substitute back huh
 one year ago

vf321Best ResponseYou've already chosen the best response.1
As @JamesWolf showed for you,
 one year ago

vf321Best 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.
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.0
ive been an idiot int he first step
 one year ago

vf321Best ResponseYou've already chosen the best response.1
@JamesWolf no, you inadvertently put up my proof.
 one year ago

sara12345Best 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
 one year ago

lgbasalloteBest 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
 one year ago

vf321Best ResponseYou've already chosen the best response.1
@sara12345 yes you're right, sorry.
 one year ago

JamesWolfBest 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
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
oh so you take the negation of q then proceed from there?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
anyway...is my proof right?
 one year ago

sara12345Best 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
 one year ago
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