by ohthatpatrick Fri May 16, 2014 1:06 pm
H1 --> L1
does not mean the same thing as
H2 --> L2.
Let's say
Boat 1 contains L.
Boat 2 contains H.
That would contradict a rule that said
H2 --> L2
But that doesn't contradict the actual rule we were given
H1 --> L1.
Reading this rule, we would just think, "is H in boat 1? Nope." and thus the rule would disappear. A conditional rule only has any meaning if the left side idea is happening. If you know the left side idea is not happening, then the rule is just inapplicable and disappears.
You're correct that if we're given
H1 --> L1
that we do not know
L1 ---> H1
This is an illegal reversal of the original statement.
Conditional statements can't be just reversed or negated.
For instance, it's true to say:
IF I'm in Los Angeles, THEN I'm in California.
But reversing that statement isn't true:
IF I'm in California, THEN I'm in Los Angeles
(If I'm in Cali, I could be in hundreds of other Californian cities)
And negating the original statement isn't true:
IF I'm not in Los Angeles, THEN I'm not in California
(that's not valid ... if I'm in San Francisco, then I'm NOT in Los Angeles but still in California)
But we CAN reverse AND negate to get a true statement:
IF I'm not in California, THEN I'm not in Los Angeles.
That move, reversing AND negating, is called creating the contrapositive. You're going to see about 20 to 30 conditional statements on every LSAT. You want to get into the habit of always thinking through and/or writing down the contrapositive, especially because LSAT is specifically testing you on whether you understand that you CAN'T just negate, CAN'T just reverse, but CAN reverse-and-negate.
So what's the contrapositive of
H1 --> L1?
(reversed and negated)
~L1 --> ~H1
(those tildes mean NOT-L1, NOT-H1)
Well, when you're dealing with a binary option, like you MUST either be in boat 1 or boat 2, saying that "L is NOT in Boat 1" is identical to saying "L is in Boat 2".
So savvy test-takers write
L2 --> H2
instead of
~L1 --> ~H1
So when we write
H1 --> L1 in this game, we should also write its contrapositive
L2 --> H2
Hope this helps