Statement I is accurate. The RNA world hypothesis posits that RNA served as the initial genetic material, capable of both information storage and catalytic activity. RNA's inherent reactivity renders it unstable and susceptible to degradation. Statement II is also accurate. DNA developed from RNA and exhibits greater stability due to its double-stranded structure, which facilitates complementary base pairing and mutation protection. DNA's structure, combined with repair mechanisms, confers superior stability compared to RNA. Consequently, both Statement I and Statement II are deemed correct.