Question

Write the suitable quantifier for all values of $x$ there is no real number such that $x^2+2x+2=0$

• A. Universal quantifier $\left(\forall \right)$
• B. Existential quantifier
• C. Both
• D. None

Answer 1

Answer: (A)

Universal quantifier $\left(\forall \right)$

Solution of an eqn $a{x}^2+bx+c=0$ are given by $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
So, Solutions of eqn $x^2+2x+2=0$ are $\frac{-2\pm \sqrt{2^2-(4\times 1\times 2)}}{2}=\frac{-2\pm \sqrt{-4}}{2}$ which are not real values.
An universal quantifier is a symbol or a logic to denote that the statement is true for all values under the scope.
As, the statement had the solutions of the given eqn as no real values of $x$, the quantifier which is best suitable is Universal.