Discrete Mathematics logic questions

In summary, the first statement "Vicky is not clever" is not a mathematical proposition because it is subjective and cannot be proven true or false. For example, some people may consider Vicky clever while others may not. The second statement "a^2+b^2=c^2" is not an indeterminate proposition because it is a true statement according to Pythagoras theorem. Lastly, the negation of "If a triangle has two equal angles it is isosceles" is "Not all triangles with two equal angles are isosceles" because the original statement refers to a specific type of triangle, while the negation refers to all possible triangles with two equal angles. Your logic is correct, but the wording for
  • #1
unknown physicist
21
0

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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  • #2
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.
 
  • #3
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?
 

FAQ: Discrete Mathematics logic questions

1. What is Discrete Mathematics?

Discrete Mathematics is a branch of mathematics that deals with mathematical structures that are countable or finite, as opposed to continuous mathematics which deals with uncountable or infinite sets.

2. What is logic in Discrete Mathematics?

In Discrete Mathematics, logic is the mathematical study of reasoning and argumentation. It deals with the principles of valid reasoning and inference, and how to construct and evaluate logical arguments.

3. What are the basic concepts in Discrete Mathematics logic?

The basic concepts in Discrete Mathematics logic include propositional logic, predicate logic, sets, functions, relations, and proof techniques such as mathematical induction and proof by contradiction.

4. How is Discrete Mathematics logic used in computer science?

Discrete Mathematics logic is used in computer science to analyze and design algorithms and data structures, to reason about the correctness and complexity of programs, and to model and verify digital circuits and systems.

5. What are some real-world applications of Discrete Mathematics logic?

Some real-world applications of Discrete Mathematics logic include cryptography, network routing algorithms, database design, scheduling problems, and artificial intelligence. It is also used in fields such as economics, linguistics, and philosophy.

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