Basic Logic

Table of contents

  1. Basic Logic (this page)
  2. Combining Logical Statements
  3. Necessary and Sufficient Condition Errors
  4. Contrapositives
  5. How to diagram conditional statements
  6. Common conditional words
  7. When to diagram
  8. Assume LSAT statements are true

LSAT Logic

Don’t worry: you don’t need very much formal logic to succeed at the LSAT. But the bit you do need will be highly useful. In this section, I’m going to teach you the following concepts, and how to use them:

  • Sufficient and Necessary Conditions
  • Contrapositives
  • Premises vs. Conclusions

Sufficient and Necessary Conditions

These are easy to understand, but difficult to master. Take the following sentence:

“All cats have tails”.

Knowledge that something is a cat is “sufficient” to tell you that it “necessarily” has a tail. “Cat” is the sufficient condition, and “tail is the necessary condition. This can be expressed many ways:

  • If something is a cat, then it has a tail
  • Every cat has a tail
  • Surveying the global cat population, you will ineluctably* discover them to have tails

Logical Diagrams

These sentences can all be expressed as a diagram: C –> T

Sufficient conditions go on the left, and lead to the necessary condition on the right – always following the direction of the arrow.  You should diagram most logical statements until you get the hang of it; it brings a lot of clarity.

Let’s try a couple more:

  • Tomatoes are red = T –> R
  • Dolphins are inevitably found in the oceans = O –> D

Careful; many people get the dolphin one backwards. Word order doesn’t matter. Inevitably means necessarily: In the oceans you will necessarily find dolphins. So Oceans is the sufficient condition.

Let’s call diagrams such as O –> D “if….then” statements (if there is an ocean, then there are dolphins), or logical statements.

Next: Combining Logical Statements

*LSAT test writers love to throw fancy words like “ineluctably” at you.  It’s a trick; you almost never need to know the word to understand the sentence.  When you see a word you don’t understand, don’t just skip by it.  Instead, slow down, and try to understand the sentence from context.  Usually, you’ll get it just fine.

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