Solution to 20. Determine the truth value of each statement if the domain consists of all real … - Sikademy
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Archangel Macsika

20. Determine the truth value of each statement if the domain consists of all real numbers. (4 pts.) a) ∃𝑥(𝑥3 = −1) b) ∃𝑥(𝑥4 < 𝑥2) c) ∀𝑥((−𝑥)2 = 𝑥2) d) ∀𝑥(2𝑥 > 𝑥)

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a) \exists x (x^3=-1)

This is true, x=-1

b) \exists x\ (x^4<x^2)

This is true, x=\tfrac{1}{2} and we have x^4=\tfrac{1}{16}<\tfrac{1}{4}=x^2

c) \forall x\ ((-x)^2=x^2)

This is true, (-x)^2=(-x)\cdot(-x)=(-1)\cdot(-1)\cdot x^2=x^2

d) \forall x\ (2x>x)

This is false, if we have x=-1 , then 2x=-2<-1=x

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Question ID: mtid-5-stid-8-sqid-1237-qpid-975