Are the following true or false? If false, state a correct version.
(a) f (x) is continuous at x = a if the left- and right-hand limits of f (x) as x → a exist and are equal.
(b) f (x) is continuous at x = a if the left- and right-hand limits of f (x) as x → a exist and equal f (a).
(c) If the left- and right-hand limits of f (x) as x → a exist, then f has a removable discontinuity at x = a.
(d) If f (x) and g(x) are continuous at x = a, then f (x) + g(x) is continuous at x = a.
(e) If f (x) and g(x) are continuous at x = a, then f (x)/g(x) is continuous at x = a.