Sixth grade math (number related) problem
$begingroup$
We have this statement (about rational numbers, btw):
If $m-n+p = p$ and $ m neq n neq 0$ then $ m = -n$
Is this true?
a) always
b) never
c) sometimes
The given answer is b) but:
1) this textbook often has some wrong answers and
2) this question got me really thinking...
According to the truth table of the implication if the premise is false, then the whole implication is true, no matter what the conclusion is.
In this case the premise is a conjunction of several facts, two of which are contradictory ($m = n $ and $m neq n$).
So the premise is false. And so I conclude the whole implication is true.
Then... what does that mean? I guess it means the correct answer is a).
logic education rational-numbers
asked Jan 19 at 22:18
peter.petrovpeter.petrov
5,439821
$endgroup$
add a comment |
$begingroup$
We have this statement (about rational numbers, btw):
If $m-n+p = p$ and $ m neq n neq 0$ then $ m = -n$
Is this true?
a) always
b) never
c) sometimes
The given answer is b) but:
1) this textbook often has some wrong answers and
2) this question got me really thinking...
According to the truth table of the implication if the premise is false, then the whole implication is true, no matter what the conclusion is.
In this case the premise is a conjunction of several facts, two of which are contradictory ($m = n $ and $m neq n$).
So the premise is false. And so I conclude the whole implication is true.
Then... what does that mean? I guess it means the correct answer is a).
logic education rational-numbers
asked Jan 19 at 22:18
peter.petrovpeter.petrov
5,439821
$endgroup$
add a comment |
$begingroup$
We have this statement (about rational numbers, btw):
If $m-n+p = p$ and $ m neq n neq 0$ then $ m = -n$
Is this true?
a) always
b) never
c) sometimes
The given answer is b) but:
1) this textbook often has some wrong answers and
2) this question got me really thinking...
According to the truth table of the implication if the premise is false, then the whole implication is true, no matter what the conclusion is.
In this case the premise is a conjunction of several facts, two of which are contradictory ($m = n $ and $m neq n$).
So the premise is false. And so I conclude the whole implication is true.
Then... what does that mean? I guess it means the correct answer is a).
logic education rational-numbers
asked Jan 19 at 22:18
peter.petrovpeter.petrov
5,439821
$endgroup$
We have this statement (about rational numbers, btw):
If $m-n+p = p$ and $ m neq n neq 0$ then $ m = -n$
Is this true?
a) always
b) never
c) sometimes
The given answer is b) but:
1) this textbook often has some wrong answers and
2) this question got me really thinking...
According to the truth table of the implication if the premise is false, then the whole implication is true, no matter what the conclusion is.
In this case the premise is a conjunction of several facts, two of which are contradictory ($m = n $ and $m neq n$).
So the premise is false. And so I conclude the whole implication is true.
Then... what does that mean? I guess it means the correct answer is a).
logic education rational-numbers
logic education rational-numbers
asked Jan 19 at 22:18
peter.petrovpeter.petrov
5,439821
asked Jan 19 at 22:18
peter.petrovpeter.petrov
5,439821
asked Jan 19 at 22:18
peter.petrovpeter.petrov
5,439821
asked Jan 19 at 22:18
peter.petrovpeter.petrov
5,439821
asked Jan 19 at 22:18
peter.petrovpeter.petrov
5,439821
5,439821
add a comment |
add a comment |
1 Answer
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$begingroup$
I believe this is a poorly worded math problem, sixth grade or otherwise. The statement
$$m neq n neq 0$$
is possibly meant to be something like
$$m, n neq 0$$
instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.
This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.
answered Jan 19 at 22:24
John OmielanJohn Omielan
2,740212
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
I believe this is a poorly worded math problem, sixth grade or otherwise. The statement
$$m neq n neq 0$$
is possibly meant to be something like
$$m, n neq 0$$
instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.
This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.
answered Jan 19 at 22:24
John OmielanJohn Omielan
2,740212
$endgroup$
add a comment |
$begingroup$
I believe this is a poorly worded math problem, sixth grade or otherwise. The statement
$$m neq n neq 0$$
is possibly meant to be something like
$$m, n neq 0$$
instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.
This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.
answered Jan 19 at 22:24
John OmielanJohn Omielan
2,740212
$endgroup$
add a comment |
$begingroup$
I believe this is a poorly worded math problem, sixth grade or otherwise. The statement
$$m neq n neq 0$$
is possibly meant to be something like
$$m, n neq 0$$
instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.
This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.
answered Jan 19 at 22:24
John OmielanJohn Omielan
2,740212
$endgroup$
I believe this is a poorly worded math problem, sixth grade or otherwise. The statement
$$m neq n neq 0$$
is possibly meant to be something like
$$m, n neq 0$$
instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.
This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.
answered Jan 19 at 22:24
John OmielanJohn Omielan
2,740212
edited Jan 19 at 22:45
answered Jan 19 at 22:24
John OmielanJohn Omielan
2,740212
answered Jan 19 at 22:24
John OmielanJohn Omielan
2,740212
answered Jan 19 at 22:24
John OmielanJohn Omielan
2,740212
2,740212
add a comment |
add a comment |
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