Answer to Question #251753 in Discrete Mathematics for Pung

Question #251753
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)
1
Expert's answer
2021-11-02T19:02:17-0400

Part a

x(x2=2)Here x=2  so satisfy\exist x (x^2 =2)\\ Here \space x= ∓ \sqrt{2} \space \space so \space satisfy. Ture


Part b

x(x2=1)\exist x (x^2 =1)\\

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


Part c

x(x2+2)\forall x (x^2+2*)

* These symbols are not proper of the reformulate up to the best of my knowledge x(x2x1)\forall x (x^2 \land x \not= 1) False


Part d

x(x2+x)\forall x (x^2+x)

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

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