Contrapositive Help

[mark]

Can you please help me with the contrapositive. When do you use it
to lock in on an answer? I don't understand. (Page 31)

Thank you.

[Dave Killoran]

Hi Mark,

Thanks for the message. You are going to see a lot more of the contrapositive, so over time you will grow accustomed to it, and eventually I'm certain you will be very comfortable with how it works. Here are some thoughts that might help you out.

First, I don't think of using it at specific times. Rather, I think of it as an ever present element that I know is there. When an answer matches it, then I know that and can select it with confidence.

Second, there is a contrapositive for every conditional statement, so it is always present when a conditional statement appears. The contrapositive is simply a different way of expressing the initial statement. To analogize, it is like examining a penny: both sides look different but intrinsically the value is the same. So, if the contrapositive is always there, as a student you should simply learn to be aware of that and know what it looks like mentally. For example, if I know that one of the rules is: when R is played, then T is played, I know I have a diagram that looks like this:

R ---> T

Some people then ask, should I also diagram the contrapositive, which is NOT T ---> NOT R ? My answer to that is no. If you are used to thinking that the contrapositive is always present, then you don't need to diagram it. But, if another rule or question comes up that would connect to the contrapositive, then I am ready to apply it immediately.

Does that help? Please let me know. Conditional reasoning is difficult, and a topic that I also cover in even greater depth in the Logical Reasoning Bible because a ton of Logical Reasoning questions deal with conditional statement and the contrapositive.

Thanks and good luck with the studying!

[Jon Denning]

Agree on all points above: contrapositive is a hugely important idea that is ever-present with conditional reasoning, and conditional reasoning can be pretty challenging at first so spend a good bit of time practicing with it prior to test day.

I also agree with Dave's suggestion that you need not write out every contrapositive on the LSAT; just know that contrapositives exist for conditional statements and use that knowledge to help you better analyze stimuli and answer choices. However, I found that in my own prep, especially early on with conditional reasoning, it was useful to diagram contrapositives simply to familiarize myself with their appearance/usage. Diagramming in the beginning stages helped me to build a strong foundation with conditional concepts so that by test day I was so well-versed in all aspects of conditional reasoning that diagramming was no longer necessary.

Certainly the "appropriate" amount of diagramming will vary person-to-person, but I think a good rule of thumb is to start of diagramming a lot, and scale it down as much as possible (as much as you can without reducing accuracy) as you get closer to test day.

[lemonade42]

Hi! Do contrapositives work in cause and effect relationships too? For example, A causes B. Is the contrapositive of "No B causes No A" also valid?

[Dana D]

Hey Lemonade,

With cause and effect relationships, we don't want to think in terms of contrapositives as much, although you are correct that if A causes B, you cannot have B without A (so no B, no A, as you said). However, with causal relationships we have additional factors to consider.

In a conditional relationship, you could also have B but no A. In a causal relationship, if we see B we know we must also have the cause - A.