Step 1: Understanding the Concept
Analogous organs have similar function but different structure and origin, for example the wings of insects and birds.
Step 2: Statement (II)
Because the origin is different, analogous organs do not show common ancestry. Homologous organs do. So Statement (II) is false.
Step 3: Statement (I)
Analogous organs are the outcome of convergent evolution, not its cause, so the statement as worded is treated as false.
Step 4: Compare the options
Both statements are false.
Final Answer:
Both Statement (I) and Statement (II) are false.
\[ \boxed{\text{(B) }\text{Both Statement (I) and Statement (II) are false}} \]