Q11

[samrumenos94]

Could someone help me clarify 11 please!
"If Felicia volunteers, then which one of the following must be true?"

I understood the thought process leading to (A) and guessed (A)

If F + V in --> T is out
If T is out, so is M
If M is out, so is R
If R is out, L is in

But I can't understand exactly why the others are wrong.

[ohthatpatrick]

Awesome, you basically nailed it.

Technically, your first conditional should read
F or V --> ~T

The chain of consequences we get here when F is in would be
F --> ~T --> ~M --> ~R --> L

So right now we know for sure that
In: F, L
Out: T, M, R

Who's left? S and V.

Well this is a must be true question. The only stuff we know FOR SURE is the stuff we listed about F, L, T, M, and R.

(B) says that S must be in. Why does S have to be in? In the work we just did, it didn't tell us anything about where S or V go.

Consider this scenario
In: F, L, V
Out: T, M, R, S

Check all the rules ... this is a legal scenario.

This allows us to eliminate (B), (C), and (E).

It's untrue to say that if F is in, then S must be in. We just showed a counterexample to that.

It's untrue to say that if F is in, then V must be out. We just showed a counterexample.

It's untrue to say that if F is in, then exactly four people must be in. We just showed a counterexample.

What about (D). Do we have to have 3 people in?

No, we can do what we want with S and V (as long as we abide by their rules).

We could put them both in and get
In: F, L, S, V
Out: T, M, R

It's untrue to say that if F is in, then exactly three people must be in. We just showed a counterexample.

Meanwhile, it is ALWAYS true to say that if F is in, then L is in.

It sounds like you're not 100% confident about the difference between MUST be true and COULD be true ideas.

We shouldn't be testing these answer choices to see if they were possible. All five of them are POSSIBLE. But that's not what the question is asking. POSSIBLE = could be true.

MANDATORY = must be true.

To test whether something MUST be true, you NEVER test whether the answer choice is possible. You test whether you can AVOID doing what the answer choice says.

We eliminate (B) because we can put S out without breaking any rules.
We eliminate (C) because we can put V in without breaking rules.
Etc.

Ultimately, on this must be true question, we don't need to test any of the incorrect answers. We take the initial stimulus, that F is in, see where the Inference chain takes us, and stop as soon as no more actions are MANDATORY.

On this problem, the new condition given was that F is in. Where do the rules take us with THAT new fact?

We that
F --> ~T --> ~M --> ~R --> L

Where are we left when the Inference chain has run its course?

We know for sure that
In: F, L
Out: T, M, R

Who's left? S and V. Not sure what to do with them because we weren't forced to do anything with them.

So (A) is automatically right because it's something we're SURE of. L is indeed in. It was forced to happen.

(B) and (C) are easily eliminated because we know that S and V were the leftovers who did NOT get forced into either group.

(D) and (E) are eliminated because with S and V leftover, it's unclear whether the IN group will have 3 or 4 members.

Hope this helps.

[ElizabethC601]

I am a little concerned by this post--If the conditional statement is "If Terry volunteers, than neither does Felicia nor Veena volunteers," how can it be that the contrapositive would have F and V in the sufficient as an or function? Shouldn't it be F and V--> -T?

Many thanks!

[andrewgong01]

I am a little concerned by this post--If the conditional statement is "If Terry volunteers, than neither does Felicia nor Veena volunteers," how can it be that the contrapositive would have F and V in the sufficient as an or function? Shouldn't it be F and V--> -T?

Many thanks!

Neither/nor in conditional syntax can be loosely translated as an "and" relation; not an "or" relation.

When you take the contrapositive you take the opposite of the "and"/ "or" diction. so if it was an "and" , in the contrapositive it becomes an "or" and if it was an "or" it becomes an "and" in the contrapositive.. In other words, just take the opposite.

So for "If Terry volunteers, then neither does Felicia nor Veena volunteers" you can first think of it as "If T in --> then F and V are out" (which is the same as saying neither F nor V are in since when you say neither here you really do mean that both F and V are out and closing the possibility of having just one of them being out). If you re-write the original as an "and" in the back you can actually write out two conditional syntax :
1) T in -->F out
2) T in --> V out
[since in the original statement the necessary part was an "and" relation"]

So when you take the contrapositive, it becomes If T or V is in then T is out. Recall that just because it is now "or" does not mean you choose one of the two, it also allows for both T AND V in but just T out and V in also suffices in triggering the conditional. In other words, T in V out| V in T out | T in V in| all trigger now.


Intuitively speaking, the original statement is that if I know T is in then I know F is out and V is out. This means that if I have F in regardless of V's status, I know T has to be out because if T was in then F has to be out. T and F are mutually exclusive in the "in" column. The same logic applies for if we have V is in and even if F is out I know that T can no longer be in because I can never have both T and V both in since T in means V is out regardless of F's status.


The logic chain diagram captures all of this though when you draw the contrapositive arrow so I normally don't really think of it that deeply for the contrapositive during a game