Negation Of Quantified Statement
Negation of Universal Quantification Statement
Negation statement "For all x applicable p(x)" is "It is not true that for all x apply p(x)" or in other words "there is at least one x such that p(x) is not applicable". By using the symbol, we write as follows:(∀x) p(x) ≡ (∃x) p(x)
Example:
p: All cats have a tail
p: Not really all cats have a tail.
p: There is a cat that has no tail.
p: Some cats do not have tails.
Negation of Existential Quantification Statement
Negation statement "There is x applicable p(x)" is "not true that there x applies p(x)" or in other words "For all x such that p(x) not applicable". By using the symbol we write as follows:(∃x) p(x) ≡ (∀x) p(x)
Example:
p: There is a child who likes to play ball.
p: Not true There is a child who likes to play ball.
p: All children do not like to play ball.
Similarly this article.
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The end of word wassalamualaikum wr. wb
Referensi :
- To'Ali's book math group accounting and sales
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