Q. 84.0( 3 Votes )

# Identify the quantifier in the following statements and write the negation of the statements.

(i) There exists a number which is equal to its square.

(ii) For every real number x, x is less than x + 1.

(iii) There exists a capital for every state in India.

Answer :

(i) Quantifier is "**There exists**".

__Negation of statement is__

There does not exist a number which is equal to its square.

(ii) Quantifier is "**For Every**".

__Negation of statement is__

There exist a real number x such that x is not less than x + 1.

(iii) Quantifier is "**There exists**".

__Negation of statement is__

There does not exist a capital for every state in India.

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PREVIOUSFind the component statements of the following compound statements and check whether they are true or false.(i) Number 3 is prime or it is odd.(ii) All integers are positive or negative.(iii) 100 is divisible by 3, 11 and 5.NEXTDetermine whether the argument used to check the validity of the following statement is correct:p: “If x2 is irrational, then x is rational.”The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.

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