Alright my little LSAT takers, earlier we discussed the importance of knowing the ways to combine Quantity statements in your LSAT prep. We went over how to combine an ALL statement with an ALL statement. Remember? You look to the sufficient (left) side and if they are the same you can combine them into a SOME statement."
Now let's move on to combining an ALL statement with a MOST statement. We're getting fancy now! For example:"
All women are sensible people. Most women love chocolate.
Therefore, what? Let's draw the statements out:"
All women are sensible people. (Stop rolling your eyes!)
W - S
S ? W
Most women love chocolate. (REMEMBER: MOST statements do not have contrapositives.)
W-most-C
Now take the rules you know about combining Quantifier statements and apply here. We have two Ws and W is sufficient in our sufficient and necessary statement. So let's combine them and make the sentence into a SOME statement. We get:"
Some people who love chocolate are sensible people.
C-some-S
Voila! That wasn't too difficult right? It's really important to remember that only ALL statements have contrapositives. BUT this example adds another teensy rule you need to remember: though SOME and MOST statements do not have contrapositives, you can get another true statement out of them by flipping them. You can reverse any MOST statement and as long as (1) you keep the variables the same (i.e. don't negate) and (2) you change the MOST to a SOME. Take the MOST statements from my women/chocolate example:"
Most women love chocolate.
W-most-C REVERSIBLE SO ALSO MEANS:
Some people who love chocolate are women.
C-some-W
Why does that matter? Well you can only combine ALL with MOST or SOME if the arrow (i.e. the S & N statement) points away from your Quantifier statement so sometimes switching a MOST into a SOME statement can help you."
Going back to our example, reversing our MOST statement allowed us to combine these statements to arrive at our conclusion that "some people who love chocolate are sensible people.""
C-some-W ? S
C-some-S
You can also flip SOME statements into SOME statements! For example:"
Some cherries are sour.
C-some-S
CAN ALSO MEAN:
Some sour things are cherries.
S-some-C
Easy, right? Let's try out one more example:"All cats have whiskers. Most cats have pointed ears. Some animals with whiskers have tails.
What can we conclude? Well..."
All cats have whiskers.
C - W
W ? C
Most cats have pointed ears.
C-most-P
Some animals with whiskers have tails.
W-some-T
We can then deduce from this information that, "Some animals with pointed ears have whiskers," or "Some animals with whiskers have pointed ears."
C-most-P
P-some-C ? W
P-some-W REVERSIBLE SO ALSO MEANS:
W-some-P
Alright! I hope that was helpful! Soon we will conquer these Logical Reasoning questions!"
Happy Studying!"