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The discussion focuses on understanding how to express truth values related to quantifiers in mathematical statements. Participants emphasize the importance of translating statements accurately to determine their truth or falsity. It is clarified that if a statement is true, it should be stated as such, while a false statement requires a counter-example. The example provided illustrates how to apply this reasoning to specific integers, prompting further thought on the implications of the statements. Mastery of these concepts is essential for effectively addressing quantifier-related questions.
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Re: quantifiers

What progress have you made on any of these?
Can you tell us what sort of help you need?
 
Re: quantifiers

in these i don't understand how to express the answer of any of the following ,can i tell all the truth values or some single,if so then how
 
Re: quantifiers

annie said:
in these i don't understand how to express the answer of any of the following ,can i tell all the truth values or some single,if so then how

Well then, you must spend some time learning to translate each statement. That is the first step.

For example: the statement in a) says "for any integer $$n$$, there is some integer $$m$$ such that $$n^2<m$$.
Is that true or false?
 
Re: quantifiers

i understand the symbols and the meaning of the statements but i want to know the answer is only true or false or i have to give counter example to express it completely
 
Re: quantifiers

annie said:
i want to know the answer is only true or false or i have to give counter example to express it completely

If the statement is true then say so.
If it is false then give a counter-example.
 
Re: quantifiers

Plato said:
For example: the statement in a) says "for any integer $$n$$, there is some integer $$m$$ such that $$n^2<m$$.
You'll have to think about the meaning of these statements; there is no way around it. For example, for $n=5$, can you find an integer $m$ such that $n^2=25<m$? What about for $n=0$, $n=-5$ and every other integer $n$?
 

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