SOLUTION: Create a Euler diagram to determine whether the syllogism is valid or invalid. All football players run fast. Matt runs fast. ..Matt is a football player.

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Question 470698: Create a Euler diagram to determine whether the syllogism is valid or invalid.

All football players run fast.
Matt runs fast.
..Matt is a football player.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if we're assuming that all football players run fast, then we know that non-football players may run fast too, but EVERY football player HAS to run fast
Then we're told that Matt runs fast, so he can either be one of the football players that ALL run fast, or he can be one of the non-football players that just happens to run fast too
They've concluded that matt is a football player, which is INVALID, as proved above, because it never said that people that run fast have to be football players, just that all football players run fast

so, you can draw a circle A representing all that can run fast, then another circle B intersecting first one which contains all football players (that one is subset of all who can run fast). We are not sure where to put Matt, in intersection or A\B.