Question

Proof question help

Every room in a house has an even number of doors. Prove that there are
an even number of entrance doors to the house.

Answer 1

Have you tried induction on the number of rooms?

Answer 2

well im not sure how to use induction on this, if you know how to do this using induction, then can you please guide me through this?

Answer 3

Well first you would show that for one room, it is obviously true

Answer 4

Then you have to have a house of k+1 rooms, but you know if there were only k rooms it would be true by induction.

Answer 5

You would take away a room from you k+1 room house, and show that the number of entrances stay even, or something like that.

Answer 6

lol hahaha yea i understand how it works, its just that writing it down is hard for me cause i dont really know how to write it :(

Answer 7

Well think of it this say... say you have k room house. If you add a room, all of it's non-entrance doors were entrance doors before it was added, all of its entrance doors are new doors.

Answer 8

i see how it works but i feel like there something else i need to do besides induction

Answer 9

Ummm, is this wrong?