### Sufficient vs. Necessary Conditions on the LSAT

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“It’s confusing sufficient with necessary” is probably one of the phrases that LSAT students use most frequently. But what does that really mean? If you’re just starting out your LSAT prep, this conditional logic can be a bit confusing. So, here’s a basic lesson.

If Kate rejects Ethan’s marriage proposal, he’ll move to Wisconsin.

Many LSAT students will immediately want to turn this into letters and arrows, but let’s leave the argument as is for the moment and consider what it means. What happens if Kate rejects Ethan’s proposal? Well, off to Wisconsin he goes.  So, Ethan moving to Wisconsin is necessary if she rejects his proposal. What is sufficient to make him move to Wisconsin? A good old-fashioned rejection of his marriage proposal (by Kate) will do just fine. So, her rejecting his marriage proposal is sufficient to make Ethan move to Wisconsin. Is it the only reason he’ll move to Wisconsin? Not as far as we know. He might get a job in Madison, or perhaps he loves really fresh PBRs.

So, what does it mean if he’s moved to Wisconsin? Does it mean that Kate has rejected his proposal? It might, but it doesn’t necessarily mean that. Perhaps she’s moving there with him in holy matrimony. If you think that Ethan moving to Wisconsin means Kate rejected his proposal, you’re confusing sufficient with necessary. Another way to think of this is: you’re illegally treating the effect as a cause. Kate rejecting him is the cause (or “trigger” as I like to think), and Ethan moving to Wisconsin is the effect, result, or something that is necessary.

More formally: R –> W, (rejection leads to Wisconsin). What else can we infer (prove) from this? We cannot say that W –> R!  This is the confusion—or we can say that this is reversed logic. But, there is one other rule we can infer: If Ethan doesn’t end up moving to Wisconsin (not W, or ~ W if you want to get fancy), Kate must not have rejected his proposal. If she had rejected his proposal, then he’d be moving to Wisconsin. So, the other rule we can create is ~ W –>~ R. That’s the contrapositive of the original rule. Reverse the rule and negate (use the opposite of) each side. It’s extremely important to understand what the contrapositive is, how to form it, and how it applies to arguments and Logic Games.

If you think you have it, figure out the contrapositive of this statement:

If Liz didn’t campaign, she didn’t win the election.

Got it? Write it down.

So, the original statement can be represented as ~ C –>~ W, and the contrapositive, which we form by reversing and negating the statement, would be W –> C. That means: if she won, then she campaigned.

The million-dollar question: What can we infer if we know that Liz campaigned?

Nothing!

What we know is that if she fails to campaign, she definitely (necessarily) will not win. And we know that if she won, she must have campaigned.

A final question: If Liz did not win (the nice way of saying “she lost”), did she not campaign?

If you answered “yes,” you’ve confused necessary and sufficient. But you also cannot say “no”! All we know is 1. that if Liz doesn’t campaign, she will not win, and 2. that if she wins, she must have campaigned.

Want more help? Take a look at our LSAT books. You can get this pretty quickly! 📝

Noah Teitelbaum is a Manhattan Prep instructor based in Denver, Colorado. Noah has worked in education for years, beginning in 2001 with his first public school class in Harlem. Since then, Noah has taught mathematics at premier inner-city charter school North Star, trained teachers in New York and New Haven, and monitored human rights violations in Croatia for the United Nations. At Manhattan Prep, Noah leads the curriculum and instructor development teams. Here, Noah has re-written curriculum and books and, through regular training sessions, has maintained the renowned quality of Manhattan Prep’s instructors. Noah owns 99th percentile GMAT and LSAT scores. Interested in learning from Noah? Select your test and check out his upcoming courses here.