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Quantifiers

annie

New member
Sep 14, 2013
6
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Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196
Re: quantifiers

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

annie

New member
Sep 14, 2013
6
Re: quantifiers

in these i dont 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
 

Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196
Re: quantifiers

in these i dont 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 \(\displaystyle n\), there is some integer \(\displaystyle m\) such that \(\displaystyle n^2<m\).
Is that true or false?
 

annie

New member
Sep 14, 2013
6
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
 

Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196
Re: quantifiers

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.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,493
Re: quantifiers

For example: the statement in a) says "for any integer \(\displaystyle n\), there is some integer \(\displaystyle m\) such that \(\displaystyle n^2<m\).
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 $n$?