Discrete Mathematics logic questions

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SUMMARY

The discussion focuses on three discrete mathematics logic questions regarding propositions and their negations. The first question addresses why "Vicky is not clever" is not a mathematical proposition, highlighting its subjective nature. The second question discusses the statement "a^2 + b^2 = c^2" and clarifies that it is a definitive proposition based on the Pythagorean theorem, rather than indeterminate. The third question explains the correct negation of the conditional statement about isosceles triangles, emphasizing that "Not all triangles with two equal angles are isosceles" accurately reflects the negation.

PREREQUISITES
  • Understanding of mathematical propositions
  • Familiarity with logical negation
  • Basic knowledge of the Pythagorean theorem
  • Concept of conditional statements in logic
NEXT STEPS
  • Explore the concept of mathematical propositions in depth
  • Study logical negation and its applications in discrete mathematics
  • Review the properties of isosceles triangles and related geometric principles
  • Investigate the differences between determinate and indeterminate propositions
USEFUL FOR

Students of discrete mathematics, educators teaching logic, and anyone seeking to improve their understanding of mathematical propositions and logical reasoning.

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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