Question

Define a set X of numbers as follows.
B. 2 is in X.
R1. If x is in X, so is 10x.
R2. If x is in X, so is x + 4.
List all the elements of X that are less than 30. (Enter your answers as a comma-separated list.)

Answer 1

Just using R2 you have
{2, 6, 10, 14, 18, 22, 26, 30}
If you can multiply any of those by 10 (and have the result less than 30) Do it. Then repeatedly add 4 to that number to find the rest of the terms.

Answer 2

@DDCamp explain please, I don't understand,

Answer 3

The rules (R1 and R2) show what is in the set, based on other items in the set.

From the initial condition (2 is in the set), we know that 2+4 = 6 is also in the set. Since 6 is in the set, we know that 6+4 = 10 is in the set, and so on.

Answer 4

so, R1. R2 is rules? how about B?

Answer 5

@malia667 what do you think? is it what you need?

Answer 6

so it would be 2, 6, 10, 14, 18, 22, 26, 30 ?

Answer 7

if it so, 6*10 =60> 30, how 6 is one element?

Answer 8

oh goodness that was not right

Answer 9

B is the initial condition (where we're told to start.)

Answer 10

@Loser66 The rule says if x is in the set, so is 10x, not the other way around.

Also, the set has numbers larger than 30 (it has infinitely many) so we can't write them all down.

Answer 11

@DDCamp lesser, not larger, friend

Answer 12

@malia667 You also have to take into account R1, if x is in the set, so is 10x.
2 is in the set, so 20 must also be in the set.

Then, using R@, since 20 is in the set, 24 must be as well. And since 24 is in the set, so is 28.

Answer 13

ok i see so its, 2, 6, 10, 14, 18, 20, 24, 28, 30?

Answer 14

@DDCamp

Answer 15

Don't forget 22 and 26.

Answer 16

ok cool :)
lets see if that works...

Answer 17

hmm.. do i need 4, 8, 12 and 16 too?

Answer 18

@DDCamp

Answer 19

@terenzreignz

Answer 20

Okay, some of it would be
2 and keep adding 4 until you reach 30 (but don't include 30)
so that gives you
2 6 10 14 18 22 26
But if x is in the set, so is 10x, so
20 is in the set.
60 too, but that's already way larger than 30, so stop at 20
20...
but you still have to apply the adding-4 rule, so keep adding 4 to 20 until you reach 30
20 24 28 32 STOP, 32 is already bigger than 30

And those are it, unless I missed anything.

Answer 21

alright, that was the problem .. i was including 30! thanks buddy...

Answer 22

Okay, no problem :)