If you’ve ever been told to “mind your Ps and Qs”, you know that the expression equates to being instructed to mind your manners. That is, of course, unless you’re studying for the LSAT, where Ps and Qs have nothing to do with being polite. In fact, seeing Ps and Qs may inspire some LSAT takers to feel particularly impolite: they generally signify a conditional reasoning problem, which can be stressful and confusing for those not familiar with how conditional reasoning works. However, with a little effort, we can easily demystify the basics of conditional reasoning, so that you’re able to mind all types of Ps and Qs.
Introduction to Conditional Statements
A conditional statement is composed of an ‘if-then’ proposition and its equation is written as p → q (if p, then q), where p is a hypothesis and q is a conclusion. It’s important to remember that p and q are just placeholders and you won’t normally see those letters on the actual LSAT. Instead, you are likely to be given an if-then statement such as “If William cooks dinner, then Erin washes the dishes.” You can write that statement out in the p → q equation format: William cooks dinner → Erin washes dishes.
Now that we have laid out the basic format of a conditional statement, we need to discuss the differences between sufficient and necessary conditions. The ‘if’ or p part of a conditional statement is a sufficient condition, while the ‘then’ or q part of a conditional is a necessary condition. It’s easiest to explain the difference between sufficient and necessary conditions through examples.
Examples: Sufficient Conditions
Let’s say you walk outside and see that a car parked on the street is wet. A sufficient condition for that car to be wet would be that it just rained. Another sufficient condition would be that your neighbor is washing their car and sprayed it down with a hose. Both of these sufficient conditions explain how the car could have become wet - but neither of them are necessary for the car to have become wet, as the car could have gotten wet in other ways.
Another example would be that microwaving water is a sufficient condition to heat the water, but it is not a necessary condition, as there are other ways water can be heated that do not involve microwaving. A sufficient condition fully explains how a given outcome could occur, without being the only possible explanation for how that outcome could have resulted.
Examples: Necessary Conditions
If something is a necessary condition it means it absolutely must take place for a given outcome to occur; the outcome cannot occur without that condition being met. In order to attend a certain concert, you need tickets. Thus, having tickets is a necessary condition for attending that concert.
However, just because an outcome requires a necessary condition doesn’t mean that the necessary condition is the only thing required for the outcome to occur. For example, it may be a necessary condition for Student A to study in order to pass their math class. This means that there is no way that Student A can possibly pass math without studying. But even if Student A studies, that may not guarantee they pass their class. They may also have to take additional steps, such as going to tutoring, reading their textbook, and completing all their homework.
Examples: Sufficient + Necessary Conditions
In our if p then q equation, p represents a sufficient condition, while q represents a necessary condition. Let’s go back to our earlier example: if William cooks dinner, then Erin washes the dishes. William cooking dinner is a sufficient condition for Erin washing the dishes. There may be other circumstances in which Erin washes dishes, but William cooking dinner is one sufficient reason why Erin will wash up. However, Erin must wash the dishes in order for William to cook dinner. Since the only way William cooks dinner is if Erin washes the dishes, Erin washing the dishes is a necessary condition.
How to Master Sufficient and Necessary Conditions
Keep an eye out for ‘trigger words’ that can signify the introduction of either a sufficient or a necessary condition. Words usually associated with sufficient conditions include: if, when, whenever, every, all, any, people who, and in order to. Words commonly linked with necessary conditions are: then, unless without, until, only/only if, must, and required.
The only way to really get the hang of sufficient and necessary conditions is to practice them. In fact, you could say that practice is a necessary condition for understanding sufficient and necessary conditions. Review the examples presented in this blog post and then try writing out some examples of your own. You practice identifying sufficient and necessary conditions → you’ll be an expert at them in no time!
Stay tuned for the next post where we will begin to manipulate conditional statements with a little bit of help from renowned rapper Missy Elliott...