The easiest inference in formal logic is called the Transitive Property:

Example: You can combine like terms (B):

If A, then B: If I press the off button, then the generator will turn off.
If B, then C: If the generator is off, then the web site will shut down.

  • If A = B, and B = C, then A = C.

Valid Inference (Transitive Property): If A, then C
If I press the off button, then the web site will shut down.

The Transitive Property may not seem like a big deal, but it is. On the LSAT you are starving for rules to help you solve your questions. In the example above, the Transitive Property allowed you to increase your rules from 2 to 3. And, the LSAT has a way about testing your ability to come up with these kinds of inferences. In this lesson we’re going to eventually combine the Transitive Property and Contrapositives.

What happens when you try to contrapose conditionals joined by conjunctions (and, or)?

“And” Conditionals

Conditional statements sometimes have multiple entities for the sufficient or necessary joined by an and. When negating you have to turn it into an or.

Next LSAT: January 26

“Or” Conditionals

When two conditionals are joined by an or, you contrapose it into an and.

Magician of Contraposition

This video consolidates everything we’ve covered. Watch how he contraposes conditionals joined with and. He pulls inferences like rabbits out of a hat. This is a challenging video so you might want to watch it twice.

Sherlock Holmes on Inferences

Every problem is absurdly simple when it is explained to you.

200 seconds of blazing inferences

SHERLOCK
0:16
Conclusion: Watson does not want to invest in South African securities.
1:06 Chalk between thumb to ease cue => play billiards.
1:30 Billiards => Thurston. Thurston => ask to invest in expiring option in South Africa.
1:44 Did not ask for checkbook => not invest in expiring option.
Therefore, he turned down the investment

WATSON:
2:09 No cases => Sherlock homes has “black moods”
Contrapositive
2:29 Sherlock Holmes is cheerful => has a case

 

Next LSAT: January 26