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I need a little help deciphering my text. It says as follows :
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a) Some men are soldiers.
b) All men are hungry.
More formally these are stated :
a)\exists_{x} p, where x belongs to the set of men and p is the proposition : x is a soldier.
b)\forall_{x},where x belongs to the set of men and q is the proposition : x is hungry.
The correct negations of the above propositions are:
a)All men are not soldiers, or: \forall_{x}[~p]
b)Some men are not hungry, or: \exists_{x}[~p]
You should examine carefully the reasons for rejecting the following statements as suitable negations.
a)Some men are not soldiers.
b)All men are not hungry.
Remember that the negation of a true proposition must be false.
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They say that the negation of a true proposition must be false. Like " All men are hungry.(true)" then, "All men are not hungry.(false)" Why can't we use that? Its negation appears to be false. Can anyone give me a better explanation? Also, would a truth table help me here?
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a) Some men are soldiers.
b) All men are hungry.
More formally these are stated :
a)\exists_{x} p, where x belongs to the set of men and p is the proposition : x is a soldier.
b)\forall_{x},where x belongs to the set of men and q is the proposition : x is hungry.
The correct negations of the above propositions are:
a)All men are not soldiers, or: \forall_{x}[~p]
b)Some men are not hungry, or: \exists_{x}[~p]
You should examine carefully the reasons for rejecting the following statements as suitable negations.
a)Some men are not soldiers.
b)All men are not hungry.
Remember that the negation of a true proposition must be false.
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They say that the negation of a true proposition must be false. Like " All men are hungry.(true)" then, "All men are not hungry.(false)" Why can't we use that? Its negation appears to be false. Can anyone give me a better explanation? Also, would a truth table help me here?