(adsbygoogle = window.adsbygoogle || []).push({}); Incorrect Theorem:

Suppose x and y are real numbers and x + y = 10, then x != 3 and y != 8.

(a) What’s wrong with the following proof of the theorem?

Proof. Suppose the conclusion of the theorem is false. Then x = 3 and y = 8. But then x + y = 11, which contradicts the given information that x + y = 10. Therefore the conclusion must be true.

(b) Show that the theorem is incorrect by finding a counterexample.

So according to the answer it's false because x != 3 can't be proven with x = 3 because that's not the negation, but even so, isn't the theorem true because 3 + 8 = 11 which does contradict the premise... I'm very confused by this....

For b, the counter example was x = 3 and x = 7 but how does that disprove it? I'm still very confused by counter examples.

So would it be written as "Suppose x and y are real numbers and x + y = 10, then x = 3 and y = 7" Is that how the counter example would be written?

Please explain!

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# Disproving an incorrect theorem?

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