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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0but whats the question ?

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.1the statement in the blue box

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

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

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

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

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

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

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

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

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1All 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

sara12345
 3 years ago
Best ResponseYou've already chosen the best response.3Given : 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

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

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.1@sara12345 how is that contradiction

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

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

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.1i was referring to your solution

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

JamesWolf
 3 years ago
Best ResponseYou've already chosen the best response.0if 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

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

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

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

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

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

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

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.1if 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

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

JamesWolf
 3 years ago
Best ResponseYou've already chosen the best response.0yes 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

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

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.1anyway...is my proof right?

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