Identify the quantifiers in the following statements:

i. There exists a triangle that is not equilateral.

ii. For all real numbers $x$ and $y$ , $xy=yx$ .

iii. There exists a real number that is not a rational number.

iv. For every natural number $x$ , $x+1$ is also a natural number.

v. For all real numbers $x$ with $x>3$ , $x^2>9$ .

vi. There exists a triangle that is not an isosceles triangle.

vii. For all negative integers $x$ , $x^3$ is also a negative integer.

viii. There exists a statement in the above statements that is not true.

ix. There exists an even prime number other than 2.

x. There exists a real number $x$ such that $x^2+1=0$ .

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Quantifiermeansaphraselike\text{'}thereexists\text{'},\text{'}forall\text{'}and\text{'}forevery\text{'}etc.\\ \left(i\right)Thereexists\left(ii\right)Forall\\ \left(iii\right)Thereexists\left(iv\right)Forevery\\ \left(v\right)Forall\left(vi\right)Thereexists\\ \left(vii\right)Forall\left(viii\right)Thereexists\\ \left(ix\right)Thereexists\left(x\right)Thereexists\end{array}$