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I am a little confused by the word "assignment". The dictionary says it refers to a piece of work that is given to someone as part of their job. For example, Tom assigns something to me. In other words, I am going to do the assignment. When I communicate with Tom, which possessive pronoun should I use? The task is assigned by Tom; I think it is reasonable to say "Tom's assignment" or "his assignment". On the other hand, I am supposed to handle this task; I think it makes sense to say "my assignment". It beats me.

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    Logically, either makes sense, as you say. If there is a need to differentiate between assigner and assignee (usually 'I've got an assignment to do by Friday' etc would be clear enough), an introductory sentence would be used to give the context: 'I've got assignments from Professor Plum and Professor Huggle to finish by next weekend. I'm working on Plum's assignment tomorrow.' – Edwin Ashworth May 14 '13 at 7:42
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    Exactly as Edwin said. The assignment can be VIEWED as belonging to either the person who assigned it or the person who is tasked to perform it. In a sense, it belongs to both of them. Generally, however, I would suggest that once it is assigned, the possession transfers preferentially to the person who is going to do the task. This is similar to giving a gift; if Tom gave you a gift, it was Tom's gift because he was the giver, but it's yours now because you OWN it. – John M. Landsberg May 14 '13 at 8:23
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    So long as the specific designation of 'assignment' is given to the task, it would clearly be my assignment (think of it as 'this assignment is now my responsibility.') On the other hand, among various tasks given to you by several people, when referring to the one given by Tom, you call it Tom's assignment in the sense 'assignment given (to me) by Tom'. Context matters. HTH. – Kris May 14 '13 at 8:51
  • Assignment is another example of a Picture Noun, and similar problems arise in possessive references. There are several possible possessors and there are situations where each is relevant, so the simple form is predictably ambiguous. – John Lawler May 14 '13 at 14:38
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    I think above comments are more useful or easier to understand, compared to the answer below, which is formally expressed with many terminologies. – Jiancheng Zou May 15 '13 at 3:17
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In contractual terms, what you have here is an example of a unilateral contract. Whereas in a bilateral contract (far more common than a unilateral contract) there is a promise for a promise; in a unilateral contract there is a promise in exchange for some completed action.

When law enforcement, for example, offers a reward for information that leads to the arrest and conviction of a man on the FBI's Most Wanted List, there is a unilateral contract: If you give us the information that leads to the arrest and conviction of the criminal (the completed performance), we'll pay you $10,000 (the reward). In other words, there is a promise for a completed performance.

Similarly, when a colleague (or boss) gives you an assignment, in effect he "promises" to "reward" you with a thank you, or a "Well done!", or "I appreciate that!", or perhaps "Good. Here's another assignment," but only after you complete the assignment. By the way, if the assignor is your boss, the "consideration" (the agreed-upon reward) is that you get to keep your job, and your boss gets a completed assignment, which is his reward.

Again, in legal terms, what you have here are an offeror (the one who is giving the assignment) and an offeree (the one accepting the assignment). They come to a meeting of the minds regarding

who initially possesses what assignment,

who then gives the assignment to whom to possess,

and who in turn gives the completed assignment to whom to possess.

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