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# A quick guide to conditional logic

## A quick guide to translating common prose statements into conditional logic statements

Diagramming conditional logic statements is an extremely useful strategy often employed by high-scoring students. However, diagramming these statements accurately—a crucial skill—can be a challenge due to the many ways that sufficient and necessary conditions can be presented in prose.

You may find it useful to make flashcards of the conditional logic statements you currently struggle to diagram. We’ve added notes for statements that tend to present the most challenges to test takers. Below the translations we've included some exercises for you to practice with!

When the condition is long or involved, it can be a good idea to use shorthand. Just make sure not to use so much shorthand that you lose track of what your abbreviations are short for!

### If X, then Y

X $\to $ Y

$\to $

*not*Y*not*X### X if Y

Y $\to $ X

$\to $

*not*X*not*Y### X only if Y

X $\to $ Y

$\to $

*not*Y*not X*### Only X are Y

Y $\to $ X

$\to $

*not*X*not*Y### Any X is/are Y

X $\to $ Y

$\to $

*not*Y*not*X### Every X is Y

X $\to $ Y

$\to $

*not*Y*not*X### No X is/are Y

X $\to $

Y$\to $

*not*YY

*not*X### X cannot be Y

X $\to $

Y$\to $

*not*YY

*not*X### Without X there can be no Y

Y $\to $ X

$\to $

*not*X*not*Y### X requires Y

X $\to $ Y

$\to $

*not*Y*not*X### In order for X to be true, Y must be true

X $\to $ Y

$\to $

*not*Y*not*X### X depends on Y

X $\to $ Y

$\to $

*not Y**not*X### X happens whenever Y happens

Y $\to $ X

$\to $

*not*X*not*Y### No X unless Y

X $\to $ Y

$\to $

*not*Y*not*X### Your turn!

We'll provide you with some examples from actual, previously-administered LSATs. Think about how you'd translate each one into conditional logic, then click the link below to reveal the answer and check your work.

If you find yourself struggling, refer back to the patterns above, and, if you made flashcards, make sure that you keep that specific flashcard on hand until you eventually feel comfortable with the translation.

- If Joan had gotten an A on her paper, she could pass the course without doing the presentation.

- People can feel secure if they are governed by laws that are not vague.

- Knowledge can be gained only if medical consent is sometimes bypassed.

- Only propositions that can be proven true can be known to be true.

- Any moon, by definition, orbits a planet.

- Every student who walks to school goes home for lunch.

- No strictly physical theory can explain consciousness.

- Fitness consultants who smoke cigarettes cannot help their clients become healthier.

- Without self-understanding it is impossible to understand others.

- Novelists require some impartiality to get an intuitive grasp of the motions of everyday life.

- In order to understand Stuart’s art, Robbins must be able to pass judgment on it.

- The existence of a moral order depends upon human souls being immortal.

- Inflation occurs whenever the money supply grows more than the production of goods and services grows.

- Ann would not quit unless she were offered a fellowship.

### Takeaways

- Conditional logic shows up in some Analytical Reasoning rules and some Logical Reasoning passages. Strength and confidence in this area can give you an edge on Test Day.
- Refer back to this article often if you find yourself mistranslating statements. If you are the type of student who works well with flashcards, go ahead and make flashcards from this article!
- Translate the
*logical meaning*of statements—don't translate word by word without considering whether the logic matches the sufficient and necessary conditions you've chosen. - Trigger (the condition on the left) and Result (the condition on the right) simply means that if I know that the condition on the left is true, then I 100% also know that the condition on the right is true (it already happened, is happening, or will happen). Timeline doesn't matter in conditional logic. The only thing that matters is which event is sufficient to get to which other event.
- Conditional logic takes time and practice. It's like learning a new language. Be patient,
*don't*just give up and guess, and keep working through our other logic articles and video lessons until it all "clicks". - Lastly, get in the habit of reading our explanations carefully to learn if you've mistranslated something.

**Good luck!**

## Want to join the conversation?

- On #13 I don's understand why inflation is the necessary condition. Wouldn't "money supply grows more than production grows" be necessary for inflation to occur?(3 votes)
- The word "whenever" signals that every time (or 100% of the time) that the money supply grows more than production grows, inflation occurs. So, money supply growth exceeding production growth guarantees that inflation occurs - it is sufficient.(4 votes)

- #10 do not understand the contrapostiive

Novelists require some impartiality to get an intuitive grasp of the motions of everyday life.

[Hide explanation]

intuitive grasp →\rightarrow→right arrow impartiality

partiality →\rightarrow→right arrow no intuitive grasp

Remember: The goal is the sufficient condition (on the left), while the requirement is to the right of the arrow. That’s because if a goal is met, then you can be certain that the requirement for the goal must also have been met.(4 votes) - dont understand

Ann would not quit unless she were offered a fellowship.

[Hide explanation]

Ann quits →\rightarrow→right arrow Ann was offered fellowship

Ann not offered fellowship →\rightarrow→right arrow Ann doesn’t quit

Remember: “Unless” doesn’t indicate a trigger! It always indicates a necessary condition. Here, Ann could be offered a fellowship and still not quit. Being offered a fellowship is necessary for her to quit—but it doesn’t guarantee anything.(3 votes) - For any moon, by definition, orbits a planet, isn't orbits a planet the trigger and so it has to be on the right?(3 votes)
- I'm really confused by this translating common prose statements to conditional logic statements. Is there any shortcut to quickly guess the right format?(3 votes)
- So....

Knowledge can be gained only if medical consent is sometimes bypassed

is different than

If medical consent is bypassed, we can gain knowledge

?(3 votes) - If X happens whenever Y happens, shouldn't it be X -> Y, since Y is the trigger and the trigger is usually on the right side of the arrow?(2 votes)
- it corn, a big lump of knobs(2 votes)
- What is the contrapositive if it is something like:

If A → B AND C

If A → B OR C

If A AND B → C

If A OR B → C(1 vote)- 1.if a👉b and c = if not b or not c， not a

2.if a👉b or c = if not b and not c，not a

3.if a and b👉c = if not c，not a or not b

4.if a or b👉c = if not c👉not a and not b(1 vote)

- I'm confused by the contrapositive to #2:

People can feel secure does not mean that people**do**feel secure, just that there is a possibility that they might. Also, feeling secure is not the same as being secure. People may feel secure if there are vague laws but they have a very big gun, or a magic forcefield, for example.

I suggest the contrapositive is:**can't feel secure -> not governed by not vague laws**(1 vote)