Formal:
* "The CEO presented a big proposition to the board, proposing a merger with our biggest competitor."
* "The new law presents a big proposition for our company, requiring significant changes to our operations."
* "The scientist's big proposition was that climate change could be reversed through a new type of technology."
Informal:
* "Moving to a new city is a big proposition, but I think it's the right move for my family."
* "Asking her to marry me is a big proposition - I'm hoping she says yes!"
* "Starting my own business is a big proposition, but I'm ready for the challenge."
In these examples, "big proposition" means:
* A significant proposal or idea: This could be a business deal, a policy change, or a personal decision.
* Something challenging or risky: The proposition might require a lot of effort, investment, or commitment.
* Something with the potential for great reward: The outcome of the proposition could be highly positive, even if it's risky.
Remember, "big proposition" is an informal expression, so use it appropriately depending on the context.