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we have to prove two things? : 1) 3n+2 is even , 2) n is even

no, it's prove n is even GIVEN 3n + 2 is even.

ok , thanks

If 3n + 2 is even, then 3n is even

if 3n is even then n is even.

Given : 3n+2 is even
To prove : n is even
3n+2 = 2k
3n = 2k-2
3n = 2(k-1)

not true for n=1 ?
3+2=5<---not even

IF 3n+2 is even , prove that is even. @hartnn

But it's not so no guarentee is made.

lets clear it from @lgbasallote what the exact question is...

Just out of interest whats the general way to prove something is even, divide by 2?

yes

if we prove a number is of form 2k that proves it is even

right I see

but whats the question ?

the statement in the blue box

forgot to mention by the way....that the direct proof done here was wrong

they took n as the condition... 3n + 2 is supposed to be the condition

so 3n + 2 = (a different n)?

if you use direct proof...
it should be 3n + 2 = 2x
then prove n is even

but like i said...should be contradiction though

well okay thats easy enough, too

hmmm then let's see you try

@sara12345 you cannot say "assume that n is odd" and then equate it to 2k

@sara12345 how is that contradiction

we do that always in proof by contradiction

RHS = even , LHS = odd => contradiction

i was referring to your solution

How can you prove that it equals 2k, though?

hmm seems legit

so in proof by contradiction...you still substitute back huh

As @JamesWolf showed for you,

no its not legit

ive been an idiot int he first step

@JamesWolf no, you inadvertently put up my proof.

@sara12345 yes you're right, sorry.

oh so you take the negation of q then proceed from there?

anyway...is my proof right?

lgba ur proof is more correct as it shows the assumption n is odd as well by letting n =2k+1