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 , it's x=-1.
(b) True. has no solutions so . So yes, there is x in R such that .
(c) True. No matter what x is, .
(d) False. . So this statement is true only for positive numbers, not for all x in R