Valid vs. Invalid argument forms

[LSAT student]

Hello, I just wanted to find out if the conclusions in these two scenarios are both valid?

A B C
Therefore: A C


A B C
Therefore A C

[Beth Hayden]

Hi there,

If all As are Bs, and some Bs are Cs, that is not enough to conclude that some As are Cs. There might be extra Bs that are not also As--the arrow only goes in one direction.

I'm going to use colored marbles as an example here. Say I have 10 marbles which can all have a combination of red (A), blue (B), or yellow (C) stripes. There are 5 marbles with red and blue stripes, 3 marbles that are only blue, and two marbles that are both blue and yellow. All the red marbles are also blue (all As are Bs). Some of the blue marbles are also yellow (some Bs are Cs). None of the red marbles are also yellow (no As are Cs).

However, your second statement is valid. If most As are also Bs, and all Bs are also Cs, then you know that most of the As are Cs. Here imagine there are 9 marbles with red, yellow, and blue, then 1 marble with just red. 9/10 of the red marbles are also blue (most As are Bs). All of the blue marbles are also yellow (All Bs are Cs). 9/10 of the red marbles are also yellow (most As are Cs).

Hope that helps!
Beth