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I want to know if the word "also" do the same thing like "AND"?

For example, there's a statement like this:

All the students who are good at Maths also work hard.

Let M(x) = "x is good at Maths"

W(x) = "x work hard"

To rewrite the statement, i don't know which one is correct.

1- all students x, who is good at Maths AND works hard

2- all students x, who is good at Maths, then he/she works hard

rMath
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1 Answers1

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For this particular example, it is number 2, an implication: $$M(x)\Rightarrow W(x).$$

For all $x$ such that $M(x)$ it follows that $W(x)$. If they are good at math, then they (also) work hard.

"Also" in this usage should generally be the implication rather than AND - at least I can't think of a counterexample.

Nameless
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  • how about the statement "Some of the students who is good at Maths work hard" ? >> for some students x, M(x) AND W(x) ? Am I right? – rMath Sep 30 '13 at 15:15
  • Yes, that seems right. If you mean that not all students who are good at math also work hard. In this case $M(x)\Rightarrow W(x)$ would not be true, because it would imply that all students who are good at math also work hard (but you are saying only some of them do). – Nameless Sep 30 '13 at 19:14