-  First is the act of neglecting the second

An analogy is a comparison between two pairs of words that have a similar relationship. In this analogy, the first pair of words is "Overlook : Aberration," which implies that the first word means to ignore or fail to notice something unusual or abnormal, while the second word means an unusual or abnormal behavior.

Using the same logic, we can try to find the relationship between the second pair of words. Therefore, to condone means to accept, allow, or excuse something that is wrong or illegal, while an offense is a violation of the law or a wrongdoing.

Hence, option B is the correct answer to the given analogy as the relationship between Condone: Offence is similar to Overlook: Aberration.

Let's understand the other options and why they are incorrect:

A. Mitigate: Penitence - Mitigate means to make something less severe or painful, and Penitence means feeling sorry or regretful for one's actions. These two words do not share a similar relationship as the given pair, making option A incorrect.

C. Error: Omission - An error means a mistake, while an omission means something that is left out or not done. Although both words have a similar meaning, the relationship between the two is not the same as the given pair, making option C incorrect.

D. Conviction: Criminal - A conviction means finding someone guilty of a crime, while a criminal is a person who commits a crime. These words do not share a similar relationship as the given pair, making option D incorrect.

E. None of these - As we have already found the correct answer to the given analogy, this option is incorrect.

In conclusion, the correct answer is option B, which is "Condone : Offence," as they have a similar relationship to "Overlook : Aberration."