P: not X → not BP: B–most–AC: ?

BenjiRower July 12, 2016

Help with the question

What I got was Not x - > not B B - > X B - > most A Not most A - > not B Just don't know I'm supposed to get a conclusion about A and X from that. B - > X B - > Most A Therefore X - > most A??? Please help me with this sort of set up cause I have seen these before in daily drills but never managed to solve Best, Ben

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Mehran August 7, 2016

@BenjiRower in order to combine a quantifier statement and a Sufficient & Necessary statement, the variable that the statements share in common must be the sufficient condition in our S & N statement.

Here the variable in common is "B" and the contrapositive of P1 is:

B ==> X

We need our arrow to point away from our S & N statement, so we would want to reverse P2:

A-some-B

Then we can combine as follows:

A-some-B ==> X

To conclude:

A-some-X

Remember, quantifiers do not have contrapositives like S & N statements.

Rather, you can reverse them but remember that "most" becomes "some" when you do so.

Hope this helps! For a more in-depth discussion of these concepts, please watch our video lesson on Quantifiers.

avazeh101 November 8, 2017

Hi I had a small question concerning:
A-some-X
X-some-A

Why doesn't the "some" change into "most", why does it remain "some" after we change it into its contrapositive?

Thank you,
Avazeh

Mehran November 13, 2017

Hi Avazeh, thanks for this important question! "Some" always reverses as "some." "Most" reverses as "some," too. Hope this helps.

Madeline-BigAngel June 11, 2018

I keep having trouble with these sorts of questions, they are not clear to me. I keep listening to the taped lesson But it hasn't clicked yet. :(

Christopher June 15, 2018

@Madeline-BigAngel, try writing out the rules as you watch the video, and then practice the flash cards. You'll get there. Continuing to do daily drills can help with this too.

elaineblueville January 14, 2019

What does some or most mean here? I mean in an example of sentence?

yuetngan February 13, 2019

What do you mean 'we need our arrow to point away from our S&N statement?'

Ravi February 14, 2019

@Noname and @yuetngan,

Happy to help.

@Noname,

"some" means at least one, and "most" means at least half plus one.

B-most-A

This means most Bs are As

For example, there could be 100 Bs, and 51 or more of them are As

A-some-B

This means that some As are Bs. There could be 100 As, and at least 1 A is a B.

@yuetngan,

Great question. What Mehran means when he says "we need our arrow to
point away from our S & N statement" is that we need a statement that
can connect up to the sufficient condition of the S & N statement.
B-most-A cannot connect up to B - >X, but B-most-A can be rewritten as
A-some-B, and this has a reversible arrow that can connect up to the S
& N statement we have.

Remember all "some" statements (which we write like "-some-") are
reversible arrows.

Now, we have

A-some-B - >X, so we can conclude

A-some-X.

Remember, the goal with these problems is to make a chain that
connects all of the variables together so that we can draw
conclusions.

For more information on quantifiers, check out the video lesson to
help you absorb the concepts more.

Does this make sense? Let us know if you have any questions!

marthajanidsilva September 15, 2019

I did everything right, and got the correct chain of A -some -B-X.. now I don't know how the answer is what it is. I remove the B and the flip the order? Or remove the B and make it a contrapositive ?

rurcia August 16, 2022

So I got the answer A-some-X, but because it wasn't an option, I put no valid conclusion. It is because I still had to flip the order of A-some-X to X-some-A? How do we know when to flip the order of the answer?

Emil-Kunkin August 29, 2022

Those are actually the same statement. To say that some dogs are pets and that some pets are dogs are both saying the same thing.

PatriciaManring February 12 at 09:52PM

Why are - used?
Is it representing a negative value or subtraction formula?
Otherwise these symbols are not necessary. The dash should be replaced with a different character or symbol.

PatriciaManring February 12 at 09:54PM

How did pets come from the letters in this statement or is there part of the statement missing and not being displayed to give clarity?

PatriciaManring February 12 at 09:56PM

If these are equivalent to chromosomes for animal species then why is there a word splitting the identifier

PatriciaManring February 12 at 09:56PM

Or not splitting but interfering