Question

Stephanie is doing an indirect proof with three given statements and one conclusion. How many of these statements could be false based on her assumption to contradict the assumption and prove the original conclusion?

One

Two

One, two or three

Three

Answer 1

this is just plain confusing to me

Answer 2

This is confusing to me, too.

Answer 3

do you know anyone who could help explain?

Answer 4

@asnaseer, can you shed some light on this horribly confusing wording?

Answer 5

@dpaInc @jim_thompson5910 can you help?

Answer 6

I speculate an answer to this question. I am not so sure how to justify it.

Answer 7

ok

Answer 8

Given:

Shelly: Andrea did it.
Jess: Shelly did not do it.
Andrea: I didn't do it.

Prove: Andrea did leave the key in the door.
For an indirect proof, assume that Andrea did leave the key in the door. Assuming she did. Shelly's statement that Andrea did it is TRUE. Assuming that Andrea left the key, Jess's statement that Shelly did not do it is TRUE. Finally, assuming that Andrea didn't leave the key, Andrea's statement that she didn't do it when she did is FALSE. Since two of the three given statements contradict the assumption, the assumption is false; therefore, its opposite is true. Andrea didn't leave the key in the door.

Answer 9

yes - the wording is definitely confusing :)
Lets say she started with: One (a false assumption)
Then she could end up with Two OR Three to contradict this

Answer 10

similarly, starting with Two (a false assumption)
she could end up with One Or Three to contradict this

Answer 11

Same applies with Three

Answer 12

Does that make any sense?

Answer 13

so the answer would be "one, two or three" ?

Answer 14

remember the question is asking for how many of these statements could be FALSE.

Answer 15

so the answer is then "one" ?

Answer 16

@Limitless does this match up with your thoughts?

Answer 17

@asnaseer, no. Originally I thought it was "one, two, or three". My reasoning was that if all three are false, a contradiction is evident. If two are false, a contradiction is evident. If one is false, a contradiction is evident. You only _need_ one, though. But the question does not seem to be asking how many you _need_.

Answer 18

I'm rather confused by this question. I could honestly be wrong.

Answer 19

ah - yes "how many /could/ ..."

Answer 20

@Calcmathlete, what do you think?

Answer 21

im now lost again... is the answer "one" or "one, two or three"?

Answer 22

@LivForMusic, we're honestly not sure. You're as lost as we are.

Answer 23

the other way of looking at it is as follows:
she wants to prove One is true.
so she starts with assuming One is false
and ends up with "One, two or three" being true, thereby contradicting the original statement

Answer 24

@jim_thompson5910 @campbell_st @zepp can you help us?

Answer 25

Yup. I'm lost too...when I learned Geometry, we mainly did two-column proofs...I would go with the third choice if I had to though...

Answer 26

(This has got to be the most pinged question in all of OS history. . .)

Answer 27

For good measure: @Zarkon

Answer 28

not quiet - there have been bigger ones... :)

Answer 29

from my last reasoning:
One could be true
Two could be True
Three could be true

Answer 30

So I would say that "One, two or three" is the only statement that cannot be conclusively proved to be true starting with the assumption that it is false - does that make sense?

Answer 31

^ from what everyone is saying i agree @asnaseer

Answer 32

we need a nod from the master logician - Zarkon :)

Answer 33

I'm a tad confused. What answer choice have we concluded? You lost me there, @asnaseer.

Answer 34

"One, two or three"

Answer 35

Let's see what everyone else has to say now. :)

Answer 36

good idea - lets let it simmer for while... :)

Answer 37

he more I think about this the more I am convinced that "One, two or three" is indeed the answer. Because, to prove it wrong, we would need to conclude with "One, two AND three" are true.

Answer 38

*the more

Answer 39

ok

Answer 40

can you help me with another question... its easier i just want to know if i am right.

Answer 41

@LivForMusic is this a homework assignment? If it is, then I would be interested to know if we did indeed conclude the right answer once it has been marked.

Answer 42

i posted it. and yes it is. but its open book so thats why i am posting is on OS

Answer 43

you should post each question in the list to the left. unfortunately, it's very late here, so I need to go catch some Zzzz's now - sorry...

Answer 44

thanks @asnaseer

Answer 45

yw :)

Answer 46

the answer to this was "one, two, or three" :) so we got it correct. thank you all!

Answer 47

Awesome! You're welcome.

Answer 48

thanks for letting us know! :)