Solution to Determine the truth value of each of the quantified statements below if the domain consists … - Sikademy
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Archangel Macsika

Determine the truth value of each of the quantified statements below if the domain consists of R. (a)∃x(x^5 = -1) (b)∃x(x^6< x^4) (c)∀x((-x)4=x^4) (d)∀x(2x > x)

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(a) True. There is a x in R such that x^5=-1 , it's x=-1.

(b) True. x^6<x^4,x^4(x^2-1)<0,x^4<0 has no solutions so x^2-1<0,|x|<1,-1<x<1. So yes, there is x in R such that x^6<x^4 .

(c) True. No matter what x is, (-x)^4=((-1)\cdot x)^4=(-1)^4\cdot x^4=1\cdot x^4=x^4 .

(d) False. 2x>x, x>0 . So this statement is true only for positive numbers, not for all x in R


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Question ID: mtid-5-stid-8-sqid-3497-qpid-2196