Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
how can i disprove the following statement
\[(\exists a ,b \in \mathbb N)(3a + 4b = 2)\]
 one year ago
 one year ago
how can i disprove the following statement \[(\exists a ,b \in \mathbb N)(3a + 4b = 2)\]
 one year ago
 one year ago

This Question is Closed

UnkleRhaukusBest ResponseYou've already chosen the best response.0
maybe another method
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
negation is \((\exists a,b\in N)(3a+4b\neq 2)\)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Assuming the statement is true,\[\rm b = {2  3a \over 4}\]so\[\rm b = {1 \over 2}  {3a \over 4}\]Therefore, if \(\rm a\) is a natural number, then \(\rm b \) isn't (try it  picking 1 will get ya some idiotic negative fraction).
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Let's do the magic for \(\rm a\) as well.\[\rm a = {2  4b \over 3}\]\[\rm a = {2 \over 3}  {4b \over 3}\]If \(\rm b\) is a natural number, then you get a negative fraction and therefore \(\rm a\) is not.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
We've proved that both \(\rm a\) and \(\rm b\) don't belong to the set of natural numbers. QED
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
so i assume that \(a\) is a natural number and show that if it is; \(b\) cannot be a natural
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
i like my proof better
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
oooh i thought it said \(\forall a,b\in \mathbb{N}\) did it change or can i not see straight?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Basically, your statement says that both a and b must be natural. I've shown that in both cases, one must be a negative fraction  not belonging to the set of natural numbers.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
@satellite73 Bikes don't have a good reflector at night. That's why.
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
it must be past my bed time
 one year ago

Mr.MathBest ResponseYou've already chosen the best response.2
Or just note that \(3a+4b\ge7\) \( \forall a,b \in \mathbb{N}\). Then the statement is false since \(2<7\).
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
And by the way, that's the linear combination thingy
 one year ago
See more questions >>>
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.