So what do sufficient and necessary conditions mean, anyway?
- Louis Zatzman
- 14 hours ago
- 3 min read
One of the most common reactions when I bring up formal logic with new students is a groan. Perhaps a heavy sigh. It is often considered one of the hardest, least approachable components of the LSAT. But that is frequently because of how it is taught. I don't find sufficient and necessary conditions to be complicated, and teaching them as simple concepts really helps students understand.
First, what is formal logic? Formal logic, or conditional causation, is anything on the LSAT that is defined as always true. It is the most powerful structure because it only deals in certainties. We don't really have such things in real life. This is what separates the LSAT from reality and what allows you to be tested on logic: the concept of certainties. So formal logic exists whenever a causative relationship is absolute and generalizable. In other words, "all dogs eat bananas" is formal logic because it is absolute, whereas "some cats eat cherries" is not.
I know that other places teach a sufficient and a necessary as two components of the same condition. I find that to be overly complicated. Instead, the best way to learn them is as two different relationships.
Definitions of Sufficient and Necessary Conditions
A sufficient condition causes. The presence of the sufficient condition is enough to cause the result, but the absence means nothing (you could still have another cause).
A necessary condition means cannot happen without. The absence of a necessary condition stops the result from happening, but the presence does nothing (it is not causative).
In other words, a sufficient condition proves a positive (a result will happen), while the absence of a necessary condition proves a negative (a result won’t happen).
And each has a number of different pattern indicators. When you see these words, you should be thinking about formal logic.
Keywords and Pattern Indicators
Sufficient: Anything that is synonymous with “enough to cause.” For example:
Will happen if
Whenever
Anyone
If then
Causes
All will
None will
When this then that
Always
If will
Necessary: Anything that means “cannot happen without.” For example:
Unless
Only
Need
Cannot without
If not then not
Requires
Essential for
Prerequisite
Depends on
Except
When and How to Map Formal Logic Statements
I think in general, always map formal logic if you see at least two conditional statements with at least one variable in common. Those will be easier to figure out on paper than in your head. You’ll want to become incredibly rapid at mapping formal logic so that you don’t need to waste time figuring out what goes where.
I usually don’t map formal logic when I see it in assumption questions. Those generally intersect with normativity flaws (more on that later), so I can usually address the issue in my head without a map. But in inference and parallel reasoning questions especially, I find myself mapping more frequently.
The basic component of mapping formal logic language on the LSAT is the arrow. An arrow in formal logic indicates causation. That does not include non-conditional causation, which doesn’t always have to be true. But if you are using an arrow, it indicates that the relationship is locked in as always true. So make sure you get it right. When I’m identifying what is the condition and what is the effect of any formal logic statement, I always start with the effect -- what do I know can always be proven? It is vital to know in any formal logic statement what goes on the left-hand side of the arrow (the condition side) and what on the right-hand side (the effect side).
The general format for a sufficient condition is this:
The general format for a necessary condition is this:
So our steps for knowing how to write formal logic:
Write the arrow down.
Ask yourself, ‘what can I prove with certainty? What do I know can be caused?’ Write that down as a single variable on the right-hand side of the arrow.
Then ask yourself, ‘what will, with certainty, cause that result?’ Write that down as a single variable on the left-hand side of the arrow.
Done! Good work.
Video Example
You can translate a sufficient condition into a necessary condition, and vice versa, using a contrapositive. That is simply to reverse sides and negativities/positives for the variables. Broadly though, if you treat sufficient and necessary conditions as two different relationships, that can be turned into one another, but have different uses and purposes, the entire concept becomes much easier to understand and apply when answering questions.
