Question

Determine the truth value of each of these statements if the domain of each variable consists of all real numbers.


a. 3x (x ² = 2)


b. 3x (x ² = -1)


c. Vx (x ²+2 à ¢ ‰ ¥ 1)


d. Vx (x ² + x)

Answer 1

Part a

$\exist x (x^2 =2)\\ Here \space x= ∓ \sqrt{2} \space \space so \space satisfy$. Ture

Part b

$\exist x (x^2 =1)\\$

Since for no real number, the square can be negative. So it is false.

Part c

$\forall x (x^2+2*)$

* These symbols are not proper of the reformulate up to the best of my knowledge $\forall x (x^2 \land x \not= 1)$ False

Part d

$\forall x (x^2+x)$

Since for every real number x²+x has a solution. True