While in today's meeting is. Since the point you are trying to convey is that the assumption you made yesterday is no longer valid, the. Without an apostrophe you are indicating plurality.
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One of the answers to this question states that we shall discuss it in our today's meeting is grammatically correct. To me, that sentence is clearly wrong. I've searched but have not found any information about the origin of the phrase in this day and age. has anyone researched this?