Discrete Mathematics logic questions

AI Thread Summary
The discussion focuses on the classification of statements in discrete mathematics. The statement "Vicky is not clever" is not a mathematical proposition because it lacks a definitive truth value, while "a^2 + b^2 = c^2" is considered a true proposition rather than indeterminate, as it is a specific case of the Pythagorean theorem. The negation of the conditional statement "If a triangle has two equal angles, it is isosceles" is correctly identified as "Not all triangles with two equal angles are isosceles," emphasizing that the original statement does not imply exclusivity. Participants are encouraged to clarify their reasoning to facilitate better understanding and assistance. Overall, the thread highlights the importance of precise definitions in mathematical logic.
unknown physicist
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Homework Statement


1. Why is the statement: " Vicky is not clever" Not a mathematical proposition? Provide examples please
2. Why is the statement: "a^2+b^2=c^2 an indeterminate proposition?"
3. Why is the negation of " If a triangle has two equal angles it is isosceles" = "Not all triangles with two equal angles are isosceles" and not "if a triangle has two equal angles it is not an isosceles"?

Homework Equations


No equations, only logic for discrete mathematics class.

The Attempt at a Solution


For the first and second, I said that they are both propositions, however I stated, that the second one is true rather than indeterminate. For the last one, I stated: "if a triangle has two equal angles it is not an isosceles"
 
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Please edit your post to provide your reasons, so we can see that you made a proper attempt to answer these (rather than just guessing).

Until you show your reasoning, no one here will be able to give you any assistance.
 
unknown physicist said:

Homework Statement


1. Why is the statement: " Vicky is not clever" Not a mathematical proposition? Provide examples please
2. Why is the statement: "a^2+b^2=c^2 an indeterminate proposition?"
3. Why is the negation of " If a triangle has two equal angles it is isosceles" = "Not all triangles with two equal angles are isosceles" and not "if a triangle has two equal angles it is not an isosceles"?

Homework Equations


No equations, only logic for discrete mathematics class.

The Attempt at a Solution


For the first and second, I said that they are both propositions, however I stated, that the second one is true rather than indeterminate. For the last one, I stated: "if a triangle has two equal angles it is not an isosceles"
I said that the first and second are both propositions because being clever means that she understands things very quickly, which could be true or false, therefore a proposition. I said that a^2+b^2=c^2 is a true proposition because it is obviously shown in pythagoras theorem, therefore it is a true proposition. For the third one I wrote: " If a triangle has two equal angles it is not an isosceles" because is is the verb and I have negated the statement so I think that this is the correct place. So what is wrong with my logic?
 
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