We have all seen statements about equivalent conditions, such as If any one of the following three conditions hold, then all three conditions hold.
Are there any examples of three conditions which all hold, provided at least two of them hold? So to be slightly more concrete, given conditions (a), (b), and (c), we know that if (a) & (b) are true, then (c) is true, but if either (a) or (b) is false, then (c) need not be true. This formulation would hold up to any permutation of (a), (b), and (c).
I've given this some thought, but I really have no clue how to approach this question with rigor, although if there were a way, I feel it would be quite simple. I thought perhaps someone would know a way to demonstrate the existence or impossibility of this situation or have an explicit example.