What exactly is the difference between "introduction to" and "introduction of"?
For example: should it be "Introduction to the problem" or "Introduction of the problem"?
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There are two different meanings here:
(1) the action of introducing something
issues arising from the introduction of new technology
(2) a thing preliminary to something else, especially an explanatory section at the beginning of a book, report, or speech
a good general introduction to the subject is A Social History of England
I suspect you want meaning (2):
The first paragraph provides an introduction to the problem.
It's an introduction of a problem to the people, therefore:
Let me introduce this problem to our employees.
An introduction of this problem was made to our employees.
But, you can also say
I've been introduced to the problem.
Our employees were introduced to the problem.
It's a matter of meaning and usage.
Both of "introduction of" and "introduction to" are grammatical and have the same meaning in the following case:
Do you mind giving us an introduction of the problem?
Do you mind giving us an introduction to the problem?
But, they will have different meanings in the case below:
Your introduction to the problem will last 5 minutes. ("You" are going to be introduced)
Your introduction of the problem will last 5 minutes. (The meaning here is ambiguous: 1) "You" are going to be introduced or 2) "You" are the one who introduced the problem to others)
It's a matter of usage and meaning, some examples:
"Our students are learning English faster since the introduction of new classroom methods."
"With the introduction of penicillin, pneumonia was no longer as life-threatening as before."
"Can you give me an introduction to the president of the company?"
"Since my introduction to the use of the DVD player, I watch more movies than before."
So, for your case, "introduction of the problem" should be correct, according to first one.