2.4 - Conditional Statements

We learned in the Foundational Skills lesson that conditional statements represent a kind of contract between the condition (the "if" part) and the consequence (the "then" portion). By contract, I mean that fulfilling the condition guarantees the consequence will occur.

Here, we'll unpack conditional logic even further and how you'll encounter it on the LSAT.

In this lesson, we're covering:

• Sufficient conditions
• Necessary conditions
• The relationship between them
• A brief intro to contrapositives

Let's get to it.

Sufficient & Necessary Conditions

Students tend to get really worked up about the relationship between sufficient and necessary conditions. If this is you, don't sweat it. It's not super complicated.

I think the root of it comes from overthinking the terms sufficient and necessary themselves.

‍Sufficient just means enough. Necessary means required or inevitable.

Let's use an example involving a light switch to make this more concrete.

If I flip on my light switch, then my lights will turn on.

In this case, flipping on my light switch is enough to guarantee that my lights will turn on.

In other words, my lights are required to turn on when I flip the switch on. It's inevitable that they will turn on once I've flipped the switch on.

Sufficient Conditions: The "If" Half

Thinking back to our working definition, we call the "if" portion of a conditional the sufficient condition because it's enough (sufficient) to guarantee that the related consequence will occur.

But what happens when we don't activate the sufficient condition? 

In short, no clue!

Think back to our light switch analogy. Your gut reaction might be that if we flip the switch off, the lights would turn off. That's probably the case in real life, but not necessarily on the LSAT.

All we know for sure is that when we've met a sufficient condition, the necessary condition inevitably happens too. When we don't meet a sufficient condition, we don't know what else happens without additional information.

Necessary Conditions: The "Then" Half

We call the "then" part the necessary condition because it's required once the sufficient condition is met. It's the outcome that must occur if the sufficient condition is true.

Let's use a different example here to point out a key distinction between sufficient and necessary conditions: spilling something on the floor.

I have a four-year-old. Kids are messy. They spill stuff. So here's a conditional statement involving my kid: 

If my kid spills his water on the floor, then the floor will be wet.

Now, let's say my floor is wet. Does that mean my kid spilled his water on the floor? Possibly, but not necessarily.

There are tons of ways my floor could have gotten wet: maybe I spilled something, maybe my geriatric Beagle peed on the floor again, or maybe it's a splash of water from when I washed dishes last night—who knows?

So, what does meeting a necessary condition tell us? This leads us to contrapositives.

Contrapositives

Let's revisit the spill scenario from earlier.

If my kid spills his water on the floor, then the floor will be wet.

Assuming that the floor is wet, we can't say for sure how it got wet.

But we do learn some things. For instance, we know that if the floor isn't wet, then my kid did not spill his water on the floor. If he had, the floor would be wet. If your reaction to this was, "Duh, Brandon," then good!

All we've done is articulate the contrapositive of our original conditional statement—we expressed the same conditional a different way. That is, we took our two original conditions, flipped the side of the if-then equation they were on originally, and then negated them.

See below; I've emboldened the parts that we flipped and negated to make it crystal clear.

Original:  My kid spills his water → the floor will be wet
Contrapositive: The floor is not wet → my kid did not spill his water

Before we get too carried away with contrapositives, I want to reiterate what I said in the Advice to Avoid lesson.

Contrapositives are just one more tool in your tool belt. They're occasionally useful but you don't need them to understand arguments. They're just one more way of expressing what a conditional tell us in the first place. Use contrapositives sparingly and don't become dependent on them.

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If you take away nothing else from this lesson, remember this:

1. Sufficient means enough and necessary means required or inevitable.
2. When we meet a sufficient condition—i.e. when it occurs—we know its necessary condition must also occur.
3. Meeting a necessary condition does not mean the sufficient condition also occurred.
4. We can use contrapositives to reframe conditionals. Just flip the original conditions and then negate them.

Next, we'll take an even closer look at the relationship between sufficient and necessary.

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What should I add? What did I miss? Leave a comment below to help me improve this course for you and future test takers.