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Identify the correct statements about $2^n\ge100$. The choices are:

  1. This is a proposition
  2. This is not a proposition
  3. Its truth value depends on the value of $n$
  4. Its truth value depends on the value of $2^n$

I know this is not a proposition since the value of the variable is not determined, so choice 2. is correct. I'm certain that choice 3. is also correct, but would it be correct to say that choice 4. is correct as well?

yroc
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    In my opinion, it would be correct. – André Nicolas Sep 16 '15 at 17:24
  • @AndréNicolas I thought so. It seemed like a bit of a trick question, so I wasn't sure. Thanks! – yroc Sep 16 '15 at 17:26
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    You are welcome. It is unfortunately a bit of a trick question. In a very very formal sense, it is the variable symbol that is interpreted, making the answer no. But the context appears to be semi-formal. – André Nicolas Sep 16 '15 at 17:32

1 Answers1

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In my opinion Choice 4 is also correct. Formally speaking, it is only the variable symbol $n$ that is assigned an interpretation, and the interpretation of the term $2^n$ follows from that. But the context here is semi-formal. And in the commonsense meaning of "depends on the value of," the truth value of the formula $2^n\ge 100$ depends on the value taken on by $2^n$.

André Nicolas
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