Determine the truth value of each expression below. The domainis the set of all real numbers.
(a)
∀x∃y (xy > 0)
(b)
∃x∀y (xy = 0)
(c)
∀x∀y∃z (z = (x – y)/3)
(d)
∀x∃y∀z (z = (x – y)/3)
(e)
∀x∀y (xy = yx)
(f)
∃x∃y∃z (x2 + y2 = z2)
(g)
∀x∃y y2 = x
(h)
∀x∃y (x < 0 ∨ y2 = x)
(i)
∃x ∃y (x2 = y2 ∧ x ≠ y)
(j)
∃x ∃y (x2 = y2 ∧ |x| ≠ |y|)
(k)
∀x ∀y (x2 ≠ y2 ∨ |x| = |y|)
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