Can You Diagram These Conditional Reasoning Phrases? - LSAT and Law School Admissions Blog

Conditional reasoning appears throughout the LSAT, in the arguments presented within the Logical Reasoning sections of the test, in the grouping games that are featured in every Logic Games section, and even (to a lesser extent) in the Reading Comprehension section of the test. This type of logic classifies conditions as Sufficient or Necessary, depending on whether they are sufficient to glean further information, or necessary for something else to be true or to occur (for an expansive discussion of conditional reasoning as it applies to the LSAT, check out the new 2016 Logical Reasoning Bible). This area represents an important component of legal reasoning, of course, but more importantly from test makers’ perspective, conditional reasoning has proven to be a reliable source of confusion for test-takers.

Even when classic conditional indicator words such as “if” or “then” are included, it can be very easy to mistake the sufficient condition for the necessary. One example that I often like to use in class is the rule “Allie will be there if Brian is there.” It can be tempting to create a diagram that looks like this:

A → B

This diagram, however, does not represent the conditional statement above. It is a very common error, because of how the rule has been phrased, and because of the order in which the two conditions (Allie and Brian) have been presented. “If” introduces the sufficient indicator in this example, so the diagram should really look like this:

B → A

Did you see through that one? If so, nice work! And if you didn’t, you shouldn’t feel bad—students routinely miss it, and that’s because it’s an easy mistake to make.

Ready for more? Take a look at a few more examples, and see how quickly you can determine which condition is the sufficient one and which is the necessary:

A ticket is all that is required for entry into the festival.
If you have the necessities, then that should be sufficient.
We will leave if and when we are ready,
Your entry will be the only prize winner if, but only if, it is the only entry.
I’ll use the word “then” only if I use the word “if.”

Answers:

1. A ticket is all that is required for entry into the festival.

This is a potentially confusing example, because the word “required” is actually synonymous with “necessary,” which might lead one to conclude that the ticket is the necessary condition. However, if a ticket is all you need to get into the festival, then that ticket is sufficient for entry:

Sufficient → Necessary

Ticket → Festival

2. If you have the necessities, then that should be sufficient.

The sufficient and necessary conditions in this example are preceded by the classic indicator words “if” and “then,” respectively, reflecting the fact that “what is necessary” is the sufficient condition in this case, and of course “sufficient” is the necessary condition, leading to the following (potentially counter-intuitive) diagram:

Sufficient → Necessary

Necessities → Sufficient

3. We will leave if and when we are ready.

“If and when” is a strange but common colloquial phrase; from a conditional reasoning perspective, “if” and “when” both generally introduce sufficient conditions, so this seems somewhat redundant. What this sentence is really meant to express is that it is unclear whether an eventual state of readiness is a possibility (“if we are ready”) or a certainty (“when we are ready”), so technically, the phrase should be “if or when.” Although you will almost certainly not see this type of imprecise colloquialism on the LSAT, it would logically be diagrammed as follows:

Sufficient → Necessary

Ready → Leave

4. Your entry will be the only prize winner if, but only if, it is the only entry.

“If but only if” is a phrase that sometime confuses students, but functionally it is no different from the phrase “if and only if.” Either way, the sentence expresses two ideas: the entry will be the only prize winner if it is the only entry (only entry → only winner), and the entry will be the only prize winner only if it is the only entry (only winner → only entry). Together, these lead to the following diagram:

only winner ↔ only entry

5. I’ll use the word “then” only if I use the word “if.”

Here, the classic conditional indicator phrase is “only if,” which generally (and in this case) introduces the necessary condition, meaning that in this unusual example, “if” is the necessary condition:

Sufficient → Necessary

Then → If

So, how did you do? Still have questions on these strange examples? Post them below!

Image: Negate the Negation, courtesy of Karen Eliot

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