Drill 114 (pg. 648- 649); Questions 1, 12, 16, 20-21, 23

[Jae HeeK459]

When diagramming conditional statements, I don't understand why the word "and" is sometimes translated as "or" or why the word "or" is sometimes translated as "and." For example, question # 16: They will visit the tiger exhibit unless they visit the bear and penguin exhibits. I would diagram this as: - B and -P ---> T; -T ---> B or P. I understand the logic when I read the answer, but I don't know how to differentiate when to translate an "and" as an "and," and when not to on my own. Can someone please help me? Thank you in advance!

[Laura Damone]

Ah yes! This is quite tricky, and it hinges on the way you choose to diagram "unless" statements.

So here's the original: They will visit the tiger exhibit unless they visit the bear and penguin exhibits.

And here's the way I like to diagram it personally: NOT Tiger --> Bear and Penguin

When I see the word "unless," I think about drawing the arrow through the word. In other words, "unless" introduces the necessary condition(s). The challenging part about this approach, though, is that you have to negate the sufficient condition. Notice how the text said "they will visit the tiger exhibit" but my diagram said "NOT Tiger."

Challenging though it may be to remember to negate that sufficient condition, if you diagram "unless" statements in this way, you'll never have to guess whether you need to change "and" to "or" or vica versa. That's the reason it is my favorite approach to diagramming "unless" statements.

The approach you might have been using is to replace "unless" with "if not." When you do that, you are technically creating the contrapositive of the statement given. When you contrapose a compound conditional (Read: a conditional statement with an "and" or an "or"), you change "and" to "or" and "or" to "and." Thus, when you use the "if not" approach, you have to change the conjunction as well.

So, to diagram properly, you've got to do one of the two:

Draw the arrow through "unless," keep the conjunction, and negate the sufficient condition

- OR -

Change "unless" to "if not," and switch the conjunctions.

And if you really think about it, this makes good sense. Say I told you that you can't improve your LSAT score unless you study hard and take plenty of practice tests. That means that studying hard and taking plenty of practice tests are necessary for score improvement.

Now let's consider three hypothetical students:

Student A - neither studies hard nor takes plenty of PT's
Student B - takes plenty of PT's but doesn't study hard
Student C - studies hard, but doesn't take plenty of PT's

Will any of them improve their LSAT score? No way. Because none of them meet both of the necessary conditions. What does this prove? That failing to meet even 1 necessary condition is enough to prevent you from getting the sufficient condition. You don't have to fail to meet both.

The takeaway? -SH and -PPTs ---> -IS would be an incorrect diagram.

Instead, you need either:

-SH or -PPT --> -IS

- OR -

IS --> SH and PPT

Hope this helps!

[Jae HeeK459]

Your explanation really hit the nail on the head! Thank you!

[Laura Damone]

My pleasure!