"If you are in Tokyo, then you are in Japan." Which of these statements
MUST also be true?
๐ญ How to Think About This
In logic, every rule has a "twin" that is logically identical. Find the twin. Hint: Flip it to
the negative.
Select the logical equivalent:
Imagine you are in Osaka. You ARE in Japan. Are you in Tokyo? No.
Incorrect.
This is called the Mistaken Reversal. Just because A leads
to B, doesn't mean B leads to A.
Imagine you are in Osaka. You are NOT in Tokyo. Does that mean you are NOT in
Japan? No, you are still in Japan.
Incorrect.
This is called the Mistaken Negation. You can simply be
somewhere else in Japan.
If you aren't even in the country of Japan, is it possible for you to be in the
city of Tokyo? Impossible.
Correct. This is the Contrapositive.
The Insight: "If A, then B" is logically identical to "If
Not B, then Not A."
The Strategy: To find the logically equivalent statement,
you must do TWO things: 1. Swap the terms. 2. Negate both terms.
๐ Valid vs Invalid Moves
Valid
Contrapositive: Not B โ Not A.
"No Japan โ No Tokyo."
โ Always True.
Invalid
Mistaken Reversal: B โ A.
Mistaken Negation: Not A โ Not B.
โ Often False.
๐ค Which thinking lens(es) did you use?
Select all the lenses you used:
๐จโ๐ฉโ๐ง For Parents & Teachers
๐ฑ Real World Example
Kid: "The rule says: If you run in the hall, you get a time out."
Kid: "I didn't run. So I shouldn't get a time out!"
Parent: "That's a Mistaken Negation. You threw a stapler. You can get a time out for other
things."
Parent: "The only rule is: If NO time out, then NO running happened."
LLOS.ai uses minimal cookies to remember your preferences and improve the site. Cookie policy.
LLLOS.AI
Welcome back
Choose how you’d like to sign in. Most people use Google — it’s the fastest.