In this final article in a series of articles about LSAT Formal Logic, we will teach you what is possibly the best LSAT logic tip you can learn. We will teach you how to quickly identify which part of a statement goes with the “if,” and which part goes with the “then.” Other courses ask you to memorize large charts of possible statements, but we will teach you how to analyze any logic statement on the LSAT Test.
This lesson series covers the following articles:
Best LSAT Logic Tip
Every conditional statement has a necessary part and a sufficient part. The necessary part is something you need to get a result. Without it, the result is impossible. With the statement, “If I have no gasoline, my car will not start,” gasoline is what you need. It is the necessary part.
You will find that — when stated positively – the consequent of any conditional statement is always the necessary part. That is, you need gas to run a car. So you could phrase the statement positively (and form the contrapositive):
If my car is running, I have gasoline.
The sufficient part of a statement is the antecedent. If my car starts, that is sufficient to prove that I have gasoline. As is the case with all sufficient phrases, it’s not the only thing that could prove you have gasoline, but it’s enough to do the job. Other things would be sufficient to prove you have gasoline too, like a fuel gauge, or a recent receipt from a gas station. Any of those are sufficient to prove the car has gasoline.
- If my car is running, I have gasoline.
- If my fuel gauge is above empty, I have gasoline.
- If I just filled up my car at the station, I have gasoline.
So, what is the best LSAT logic tip? Drumroll please…
Since every consequent is necessary and every antecedent is sufficient, you could think of all conditional statements as having the following form:
If sufficient, then necessary (S –> N)
Using this formula, you can translate many casual statements into simple conditional statements, find the contrapositive and quickly scan for the right answer. Just ask yourself, “what do you need in this statement,” and put that in the consequent.
Here are some examples:
You must practice many hours to get a high score on the LSAT.
What do you need? To practice many hours.
Paraphrase: If you score high, you practiced many hours.
Contrapositive: If you didn’t practice many hours, you didn’t score high.
Only astronauts can fly the space shuttle.
What do you need? To be an astronaut.
Paraphrase: If you fly the space shuttle, you must be an astronaut.
Contrapositive: If you’re not an astronaut, you cannot fly the space shuttle.
Phil said that we won’t get into the club if we’re not dressed fashionably.
What do you need? To dress fashionably.
Paraphrase: If you get into the club, you dressed fashionably.
Contrapositive: If you didn’t dress fashionably, you didn’t get into the club.
Highway 54 is the only way you can leave.
What do you need? Highway 54.
Paraphrase: If Sam left, highway 54 was open.
Contrapositive: If highway 54 was close, Sam couldn’t leave.
Remember to keep in mind what is necessary (what do you need?) and what is sufficient (what will do the job?) in any argument. Just because an argument has words like “only” or “need” in it, don’t jump to conclusion about what is necessary and what is sufficient. Always think it out.
Strong DNA evidence was all the jury needed to convict Mr. Harris of murder.
Because of the word “needed,” you might be tempted to assume that strong DNA evidence is the necessary part of the argument. In fact, strong DNA is the sufficient part of the argument. The words “all the jury needed,” mean that DNA evidence would be enough to do the job. It’s all they need — it’s sufficient, but that’s not to say it’s the only thing they would convict on. So we know that DNA evidence is sufficient, and thus the antecedent:
Paraphrase: If the jury gets DNA evidence, they will convict Harris.
Contrapositive: If Harris is acquitted, there was no DNA evidence.
Is that completely awesome, or what? You now hold in your head the best LSAT Logic Tip around. It is the best way to quickly digest unwieldy arguments into simple conditional if-then statements that you can manipulate to your heart’s desire.
Using the Best LSAT Logic Tip with Conditional Chains
Some arguments chain one conditional statement after another. For example, what can you infer from the following argument:
Burt likes to eat apples. When he eats apples, he also drinks beer. When he drinks beer, he cries. Burt will only cry if his wife Doris is near.
First, make a paraphrase. All the statements are pretty straightforward except for “Burt will only cry if his wife Doris is near.” What do you need? Doris. Therefore, Doris is the consequent. Here is the paraphrase:
A –> B If apples then beer
B –> C If beer then cry
C –> D If cry then Doris is near
When the LSAT asks you to infer something from a chain like this, it either wants you to link the chains, or link them and take the contrapositive. There are three new things we can infer by linking these together:
A –> C If apples then cry
A –> D If apples then Doris is near
B –> D If beer then Doris is near
We can also infer their contrapositives:
Not C –> not A If Burt doesn’t cry, then no apples
Not D –> not A If Doris isn’t near, then no apples
Not D –> not B If Doris isn’t near, then no beer
Try another sample LSAT question for practice:
Scientists have long argued that the only way to end the destruction of the ozone layer is to curb the production of greenhouse gasses. Fossil fuels are the biggest contributors to the problem, so if we eliminate greenhouse gasses, we must eliminate fossil fuels. If we eliminate fossil fuels, no one can drive cars; however, cars are essential to our economic prosperity.
Which one of the following can be inferred from the argument above?
(A) By eliminating greenhouse gasses, we can ensure the protection of the ozone layer.
(B) Fuel-efficient cars could help maintain our economic prosperity.
(C) Saving the ozone layer could end our economic prosperity.
(D) If we don’t eliminate greenhouse gasses, we will continue to enjoy economic prosperity.
(E) Scientists are more interested in long-term environmental issues than in short-term economic problems.
First, by reading the question stem before reading the stimulus, you know you’re looking for an inference. Second, as you read the argument, you should recognize that you can paraphrase the argument easily as a chain of conditional statements:
…the only way to end the destruction of the ozone layer is to curb the production of greenhouse gasses.
What do you need? To curb the production of greenhouse gasses.
Paraphrase: If you save the ozone, then you end greenhouse gasses (save ozone –> no GG).
…if we eliminate greenhouse gasses, we must eliminate fossil fuels.
What do you need? To eliminate fossil fuels.
Paraphrase: If we end greenhouse gasses, then we end fossil fuels (no GG –> no FF).
If we eliminate fossil fuels, no one can drive cars.
Paraphrase: (no FF –> no cars).
…cars are essential to our economic prosperity.
What do you need? Cars
Paraphrase: If prosperity then cars (P –> C).
Notice that each statement links to the next:
Save ozone –> no GG –> no FF –> no cars –> no P*
*This was the only tricky part–we linked to “no P” by forming the contrapositive of the last paraphrase.
Answer choice (C) matches this chain. It links saving the ozone layer to an end of economic prosperity. Choice (A) affirms the consequent of the first paraphrase. Eliminating greenhouse gasses is necessary to saving the ozone, but may not be enough to guarantee it. Choice (B) is out of scope. Who knows what effect fuel-efficient cars would have? Choice (D) denies the antecedent for part of our chain.
We know from the argument that if we eliminate greenhouse gasses we won’t continue in economic prosperity. But there could be many things that keep us from that prosperity even if we don’t eliminate greenhouse gasses. Choice (E) is out of scope. It may be tempting, first because it’s hard work paraphrasing this argument and second because it seems to parallel the message of the argument. But we have no idea if there is a link between the scientists’ beliefs and the conclusions of this author.
This concludes our series on LSAT Formal Logic. Here are some summary LSAT Logic Tips to take away:
- Logical Reasoning doesn’t present you with a lot of formal statements, but creating formal paraphrases can help you understand difficult casual arguments.
- The only thing you can infer from a conditional statement is its contrapositive: If A –> B; not B –> not A
- The best LSAT Logic Tip: All conditional statements contain necessary and sufficient elements. The necessary element (what you need) is the consequent. The sufficient element (sufficient enough to prove the consequent is true) is the antecedent.
- The LSAT often chains conditional statements together. You can find contrapositives for chains as well: If A –> B; If B –> C; therefore, if A –> C, and if not C –> not A.
It’s now time to return to our LSAT Test course to choose your next lesson.