I'm in need of some help to understand the following:

1. if some K's are L's, and all L's are M's, then some K's are M's (I got this)

However

2. if all K's are L's, and some L's are M's, why is it that there would be no valid conclusion?

Also

3. let's say I reversed #1 to: if all L's are M's, and some K's are L's (I didn't change the premises, just the order it's displayed), would the conclusion be the same? Vice versa for #2

And (you'll hate this)

4.
* if something COULD BE TRUE, does that = NOT NECESSARILY FALSE and NOT NECESSARILY TRUE?
* if something COULD BE FALSE, does that = NOT NECESSARILY TRUE and NOT NECESSARILY FALSE?
* if something MUST BE TRUE, then it CANNOT BE FALSE - I got this
* if something is POSSIBLE, then something COULD BE TRUE, but does that also = COULD BE FALSE?

i guess the most important question is COULD and NECESSARILY interchangeable?

if you've been through this then you know what i'm trying to study for

 

pretty straight forward....


It's no conclusion because

all K's are L's which means that some L's are K's but some L's may not be K's
Some L's are M which mean that some M's are L's and some M's may not be M's

if all M's are L and all L's are Ks then all M's are K's
however if only some M's are L's and only some L's are K's then there could be a case of L's where you have 5 M's that are L's and 5 L's that are K's but NO M's that are K's

basicly there is no conclusions because you can't say how M's and K's are related...they may be related but they might not too.

Actually 3 does change the assumption. It says that all L's are M's and some K's are L's that means that some K's must be M's (because some K's are L's and all L's are M's)

If it could be true it's no decision. It MUST be true for it to be valid. Possible means no decision. It is only True or False or I don't know. If you can prove it could be true or it could be false then it's I don't know.

 

Sometimes it's helpful to substitute real nouns for the letters.

Let K = man, L = person, M = woman.

All men are people and some people are women. In this case, no Ks are Ms.

Let K = man, L = person, M = man.

All men are people and some people are men. In this case, all Ks are Ms.

Yes. The conjunction "and" is symmetric; i.e., "A and B" is equivalent to "B and A".

Something that could be true is not necessarily false.

Something that is (necessarily) true could be true, so (you'll love this):
something that could be true is not not necessarily true.

Similarly:

Something that could be false is not necessarily true.

Something that is (necessarily) false could be false, so:
something that could be false is not not necessarily false.

Yes.

 

It's either a critical thinking 101 class...

Or the LSAT...

Or the GRE...

I hate this stuff, even though I love Philosophy.