annie1
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The discussion revolves around understanding quantifiers in mathematical statements, specifically how to express truth values and the necessity of providing counterexamples. Participants explore the implications of statements involving integers and the conditions under which they can be deemed true or false.
Participants express differing views on whether a complete answer requires only a true or false designation or if counterexamples are necessary. The discussion remains unresolved regarding the best approach to expressing answers related to quantifiers.
Participants demonstrate varying levels of understanding regarding the translation of statements and the requirements for expressing truth values, indicating potential gaps in foundational knowledge.
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
annie said:i want to know the answer is only true or false or i have to give counter example to express it completely
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 $n$?Plato said:For example: the statement in a) says "for any integer $$n$$, there is some integer $$m$$ such that $$n^2<m$$.