Explain what the truth value is of (a) ∃x(x+ x^4= −17) (b) ∀x(4x > x^4) with logic/reasons, whereas Domain= Set of all real numbers.
Explain these statements (a) ∃x((x ≥ 0) ∧ P (x)) (b) ∀x((x ≠ 1) → P using only negations, disjunctions, and conjunctions. Whereas Domain = {-2,-5, 3, 1, 4}.
Also
Explain what the truth value is of
(a) ∃x(x+ x^4= −17)
(b) ∀x(4x > x^4) with logic/reasons, whereas Domain= Set of all real numbers.
And
Explain what is the truth value of ∃xP (x) with logic/reasons, whereas P (x) be the statement “a = a^4.”
And Domain= Set of all integers.
How would you explain these statements in terms of A(x), B(x), quantifiers, and logical connectives,
where A(x) is “x only go on big river” and B(x) is “x go on the Hudson” and Domain = Cruise ship
(a) There is a cruise ship that can only go on a big river but that doesn’t go on Hudson
(b) No cruise ship can go on big river or go on Hudson
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