uniform continuity on disjoint intervals

Question

Consider the following statements

(a) If $f$ is uniformly continuous on disjoint closed intervals $I1,I2,......,In$, then $f$ is uniformly continuous on $\cup_{j=1}^n Ij$

(b) If $f$ is uniformly continuous on disjoint open intervals $I1,I2,......,In$, then $f$ is uniformly continuous on $\cup_{j=1}^n Ij$

Which of the following is true.

(A) Both (a) and (b) are correct.

(B) Both (a) and (b) are incorrect.

(C) Only (a) is correct.

(D) Only (b) is correct.