4. Given the following two propositions about skew lines:

Proposition I: If line $a$ on plane $\alpha$ and line $b$ on plane $\beta$ are skew lines, and line $c$ is the intersection line of $\alpha$ and $\beta$, then $c$ intersects at most one of $a$ and $b$;
Proposition II: There do not exist infinitely many lines such that any two of them are skew lines. Then,
(A) Proposition I is correct, Proposition II is incorrect
(B) Proposition II is correct, Proposition I is incorrect
(C) Both propositions are correct
(D) Both propositions are incorrect
(D)
4. 【Analysis and Solution】As shown in the figure, $c$ intersects with both $a$ and $b$, so statement $\mathrm{I}$ is incorrect; furthermore, we can take infinitely many parallel planes, and on each plane, take a line such that these lines are all differently oriented, then any two of these lines are skew lines, thus statement II is also incorrect.