The phrase "with reservation" is an idiomatic expression used to indicate that one's agreement, acceptance, or approval is not complete and that there are doubts or hesitations about the situation, decision, or course of action under consideration. This phrase can also mean that there are conditions attached to one's support, acceptance, or approval.
For example, someone might say, "I accepted his proposal with reservations," implying that while they are in general agreement with the proposal, there are certain aspects of it with which they are not entirely comfortable, or that may need further consideration, before they can give their full support.
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