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amanda-fazio on September 23, 2018

Hi i have the same question. Can someone please respond? I am having difficulty with the missing premise drills as well. thanks!

Mehran on September 24, 2018

@Leanne-C @amanda-fazio let's walk through this example together to see if it helps.

P1: A ==> B
not B ==> not A

P2: ?

P3: not X ==> not D
D ==> X

C: not X ==> not A
A ==> X

Okay so notice that our conclusion here starts with "not X" (or "A" if we are looking at the contrapositive).

What does "not X" (or A) tells us in our premises?

not X ==> not D

A ==> B

But our conclusion is not "not D" (B), it is "not A" (X). How can we get to "not A" (X)?

Notice in P1 (P3), the contrapositive tells us that "not B" (D) is sufficient for "not A" (X):

not X ==> not D [gap] not B ==> not A

A ==> B [gap] D ==> X

So clearly the missing premise here is:

not D ==> not B
B ==> D

not X ==> not D ==> not B ==> not A
A ==> B ==> D ==> X

Does that help?

amanda-fazio on September 25, 2018

yes got it thank you!

Delete1 on September 25, 2018

I'm a visual learner so this answer really helped me to understand this question and others like it - thank you! I am getting closer to understanding it all and was able to finish the missing drills exercise.
However, can I see how you have solved a question like the one I have below, where what's in the conclusion isn't easily identified in the premises?:
P: A -> not C
P: not z -> A
P: ?
C: not B -> not C

When I try to apply the same reasoning from the last question I am stuck on finding how we can make the transition from not B -> (the sufficient in the conclusion) to B (not B) in the premise because it's only part of the missing premise. Thanks!

Skylar on December 8, 2019

@LeanneC, happy to help!

Here's what we're given:
P1: A -> not C
P2: not Z -> A
P3:?
C: not B -> not C

First let's find the contrapositive of each statement we're given.
P1: A -> not C
C -> not A
P2: not Z -> A
not A -> Z
P3: ?
C: not B -> not C
C -> B

Now, let's look for connections.
- We can connect P2 to P1 to get: not Z -> A -> not C
- We could also connect the contrapositive of P1 to the contrapositive of P2 to get: C-> not A -> Z

Now, let's look at these chains and how they could connect to the conclusion we're given.
- The conclusion ends in "not C" like the first chain, so we could connect these by adding "not B" to the beginning of this chain.
This would give us: not B -> not Z -> A -> not C.
This would allow the conclusion not B -> not C to be drawn.
Therefore, P3 is the connection that we made in this chain which is adding not B to the beginning. So, the missing premise would be: not B -> not Z.
- We could also use the contrapositives to connect the conclusion to the chain if that comes more intuitively to you.
Both the second chain we made and the contrapositive of the conclusion start with C, so we can connect the two by adding B to the end of the chain.
This would give us: C -> not A -> Z -> B.
This allows for the proper conclusion of C -> B to be drawn.
Therefore, the connection we added was Z -> B, so that's our answer for the missing P3.

So, the missing premise is:
not B -> not Z
Z -> B

Notice that these two statements are the contrapositive of each other. Since contrapositives have the same meaning, it does not matter which you put first as your answer as long as you have both.

Does this make sense? Please reach out with any other questions and best of luck with your studies!

Brett-Lindsay on July 2, 2020

I struggled with the missing premise questions until I found a visual shortcut. I'm sure lots of people do this already, but I haven't seen it mentioned yet.

One thing I've been doing is to take the conclusion and split it up so that one element is at the left side and one at the far right.

Then, I see what I can squeeze in from the premises. I find I can find the missing premise pretty quickly.

So, for this example, I'd take the conclusion and split it up:
not B --> --> not C

Then, I'd look at my premises and notice P1 and add it to the second last position:
not B --> A --> not C

Then, I'd notice P2 and squeeze that in:
not B --> not Z --> A --> not C

And that would give me the missing premise.

Depending on the answer choices, I might use it directly or take the contrapositive.

Hope it helps.