Understanding Conditional Sentences

The given sentence "_____ I permitted him to leave, I wouldn’t have had any problem with him being absent, _____ I?" requires us to fill in two blanks. This sentence is a classic example of a conditional sentence, specifically a third conditional, combined with a tag question.

Conditional Sentence Structure (Third Conditional)

A third conditional sentence is used to talk about hypothetical situations in the past that did not happen and their hypothetical past results. The standard structure is:

• If + past perfect (had + past participle), would have + past participle.

For example: "If I had studied, I would have passed the exam."

Sometimes, in more formal English, or to emphasize the condition, the "if" can be omitted, and the auxiliary verb "had" can be inverted with the subject. This is known as conditional inversion. In this case, the structure becomes:

• Had + subject + past participle, would have + past participle.

For example: "Had I studied, I would have passed the exam."

In our sentence, the second part of the main clause is "I wouldn’t have had any problem with him being absent," which clearly follows the "would have + past participle" structure (specifically, "wouldn't have had"). This indicates that the first part, which is the condition, should be in the past perfect form with "had" at the beginning due to the inverted structure.

Therefore, for the first blank, "Had" is the correct choice to complete the inverted third conditional structure: "Had I permitted him to leave..."

Tag Questions Analysis

A tag question is a short question added to the end of a statement. It is used to ask for confirmation or to keep the conversation going. The rule for forming tag questions is:

• If the main statement is positive, the tag question is negative.
• If the main statement is negative, the tag question is positive.

The auxiliary verb used in the tag question is typically the same as the one in the main statement, and if there's no auxiliary, "do/does/did" is used. The pronoun in the tag question matches the subject of the main statement.

In our sentence, the main clause is "I wouldn’t have had any problem with him being absent".

• The statement is negative ("wouldn't have had").
• The auxiliary verb used is "would".
• The subject is "I".

Following the rule, since the statement is negative, the tag question must be positive. Therefore, the tag question should be "would I?".

So, for the second blank, "would" is the correct choice.

Step-by-Step Solution

Let's apply our understanding to the blanks:

1. First Blank: The structure "_____ I permitted him to leave, I wouldn’t have had any problem..." indicates an inverted third conditional sentence. The past perfect tense "permitted" is used, and the result clause "wouldn't have had" confirms it's a third conditional. To form an inverted third conditional, we start with "Had". So, "Had I permitted him to leave...".
2. Second Blank: The main clause is "I wouldn’t have had any problem with him being absent". This is a negative statement using the auxiliary verb "would". For a tag question following a negative statement, we use a positive tag with the same auxiliary verb and the subject pronoun. Thus, "would I?".

Combining both parts, the complete sentence is: "Had I permitted him to leave, I wouldn’t have had any problem with him being absent, would I?"

Based on this analysis, the correct option provides "Had" for the first blank and "would" for the second blank.