Determine whether the following statements are true and give an explanation or counterexample.

a. If a function is left-continuous and right-continuous at a, then it is continuous at a.

b. If a function is continuous at a, then it is left-continuous and right-continuous at a.

c. If a < b and f(a) ≤ L ≤ f(b), then there is some value of c in (a, b) for which f (c) = L.

d. Suppose f is continuous on [a, b]. Then there is a point c in (a, b) such that f (c) = (f(a) + f(b)/2.