Synthesis of sentences

Question

So, I am given these two sentences in exam to convert into one single sentence (without changing the meaning implied the original two sentences or using and, but, so, because conjunctions) (A)

They left the door open. Expensive goods were stolen by the thieves.

Now, many fellow class mates of mine wrote (B):

Since they left the door open, expensive goods were stolen by the thieves.

But I am concerned as to whether the usage of Since is correct in the above sentence?

Like, we use Since when we are talking about a cause. Like in this sentence:

Since I have won $20 in a jackpot, I am going to spend it the way I want to!

Hence, I wrote the answer to the question as (C):

They having left the door open, expensive goods were stolen by the thieves.

In order to communicate that their leaving the door open was not the cause of thieves stealing goods. Perhaps, they might be prowling around and noticed the doors open and so just entered the house?

Therefore, my questions are:

1. Is the use of Since correct in B?
2. What's wrong with my sentence C ?

Answer 1

I applaud your very precise and scholarly distinction.

The use of since in your friend's sentence is grammatically acceptable, and it satisfies the requirements you describe. However, as you observe, it is not justified by the facts you are given.

If the exam is intended to test your reasoning ability as well as your command of English, your sentence using the absolute construction should get a better mark than your friend's.

Answer 2

The use of "since" is gramatically correct. Whether it's factually correct doesn't matter. It is true that it might not be their fault for leaving the door open, because it's not explicitly stated, but it is strongly implied that it is their fault.

"Having left the door open" sounds like a parenthetical statement, a statement that adds extra information to the sentence without changing the meaning. A parenthetical statement should be surrounded by commas. Take this sentence for example:

They let the cold air in the house.

This sentence is fine, but we could add extra information about how they let the cold air in.

They, having left the door open, let the cold air in the house.

This adds extra information, but doesn't change the meaning.

So your sentence C is wrong because it has a subject (they) but no action. If you were to take out the parenthetical phrase, you would be left with:

They, expensive goods were stolen by the thieves.

This is more clearly wrong, since the first phrase, "they" is empty, and completely out of place.