Sparkle Logic

Logic Level 1

Anything magical is dangerous.

All dragons are sparkly.

Given the above two statements are true, what would (if true) make the statement "All dragons are dangerous" true?

Anything sparkly is magical Anything magical is sparkly Anything dangerous is a dragon

Jason Dyer by Jason Dyer

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1 solution

Jason Dyer Staff
Sep 22, 2016

Using the fact that A ⟹ B ⟹ C A \implies B \implies C means A ⟹ C : A \implies C : If sparkly things are magical, dragons being sparkly implies magical implies dangerous; therefore, all dragons are dangerous.

Both "anything magical is sparkly" and "anything dangerous is a dragon" are implications going in the wrong direction to allow the transitive property to be used as needed.

8 Helpful 1 Interesting 1 Brilliant 3 Confused

But wouldn't "Anything dangerous is a dragon" true will make "All dragons are dangerous" true?

Evan Huynh - 4 years, 8 months ago

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No. I if we look at ' anything dangerous 'as a set then it will be a subset of ' all dragons'. Everything that is dangerous must be a dragon but every dragon need not be dangerous.

Anirudh Singh - 4 years, 8 months ago

the answers that just flip the word magical and sparkly are the same thing...therefore there are 2 right answers

DiShaun Williams - 4 years, 8 months ago

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"Anything magical is sparkly" is eqivilant to saying "anything that is not sparkly is not magical", and we couldn't get "all dragons are dangerous" if this statement is true.

CHIN KEE HAW - 3 years, 5 months ago

Not the best example for implication

iva vrtaric - 4 months, 2 weeks ago

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