Question

Are the following arguments valid (if so what rule does it follow?) or invalid (what's the error?)?

1 All honest people pay taxes.
Darth is not honest
∴ Darth doesn't pay taxes

2. No good car is cheap
A VX Roadster is cheap.
∴ A VX Roadster is not good

3. No vegetarians eat meat
All vegans are vegetarian
∴ No vegans eat meat.

Answer 1

1 All honest people pay taxes.
Darth is not honest
∴ Darth doesn't pay taxes

INCORRECT.
A -> B
~A may or may not give ~B
Inverse is incorrect

2. No good car is cheap
A VX Roadster is cheap.
∴ A VX Roadster is not good

Correct
Rule is aModus Tollens
a -> b
~b
-------
~a

3. No vegetarians eat meat
All vegans are vegetarian
∴ No vegans eat meat.

Correct
Rule is Hypothetical Syllogism

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