Rewrite each of the following sentences using logical connectives. Assume that each symbol!, x₀, n, x, B represents some fixed object.
(a) If f has a relative minimum at x₀ and if f is differentiable at x₀, then f′(x₀)=0..,
(b) If n is prime, then n = 2 or n is odd.,
(c) R is symmetric and transitive whenever R is irreflexive.,
(d) B is square and not invertible whenever det B = 0.,
(e) f has a critical point at x₀ iff f '(x₀) = 0 or f'(x₀) does not exist.,
(f) 2 < n - 6 is a necessary condition for 2n < 4 or n > 4.,
(g) 6 ≥ n - 3 only if n > 4 or n > 10.,
(h) x is Cauchy implies x is convergent.,
( i) f is continuous at x₀ whenever [tex]lim_{x \rightarrow x_0}[/tex] f(x) = f(x₀).,
(j) If f is differentiable at x₀ and f is increasing at x₀, then f'(x₀) > 0.