A community for students.
Here's the question you clicked on:
 0 viewing
lgbasallote
 4 years ago
Prove that if n is an integer then 3n + 2 is even, then n is even
lgbasallote
 4 years ago
Prove that if n is an integer then 3n + 2 is even, then n is even

This Question is Closed

mathslover
 4 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0no, it's prove n is even GIVEN 3n + 2 is even.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0If 3n + 2 is even, then 3n is even

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Given : 3n+2 is even To prove : n is even 3n+2 = 2k 3n = 2k2 3n = 2(k1)

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@hartnn GIVEN that 3+2 is even, n is even

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0But it's not so no guarentee is made.

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

anonymous
 4 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?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0if we prove a number is of form 2k that proves it is even

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0btw any1 here mind taking a look at my question? http://openstudy.com/updates/5078b9d7e4b02f109be44f95

lgbasallote
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0but whats the question ?

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

lgbasallote
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.1they took n as the condition... 3n + 2 is supposed to be the condition

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

hartnn
 4 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
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.1but like i said...should be contradiction though

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well okay thats easy enough, too

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0All 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Given : 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@sara12345 you cannot say "assume that n is odd" and then equate it to 2k

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0we do that always in proof by contradiction

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0RHS = even , LHS = odd => contradiction

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0How can you prove that it equals 2k, though?

anonymous
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.1so in proof by contradiction...you still substitute back huh

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0As @JamesWolf showed for you,

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you take the contradiction, show that it is not internally consistent, and therefore it cannot be true.

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@JamesWolf no, you inadvertently put up my proof.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0in 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
 4 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@sara12345 yes you're right, sorry.

anonymous
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.1oh so you take the negation of q then proceed from there?

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lgba ur proof is more correct as it shows the assumption n is odd as well by letting n =2k+1
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.