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Identify the quantifier in the following...

Identify the quantifier in the following statement and write the negation of the statements
(i) p : For every real number x,5x is greater than 5
(ii) q : There exists a prime number which is even
(iii) r : For every positive interger x,x+2, is a positive interger
(iv) s : For every planet there is a moon
(v) t : There exists a rhombus whose all angle is `90^@`

Text Solution

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Quantifier `rarr` For every
(i) ~p : There exists a real number x , such that 5x is not greater than 5
(ii) Quantifier `rarr` There exists
~q : It is not the case that a prime number which is even
(iii) Quantifier `rarr` For every
~s : There exists a positive interger x , such that x+2 is not a positive interger
Quantifier `rarr` For every
~s : There exists a planet which does not have moon
(v) Quantifier `rarr` There exists
~t : It is not the case that a rhombus whose all angles is `90^@`
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