Let P1 = {C1, C2, ... CM} and P2 = {D1, D2, ... DN} be partitions of set A. P = {Ci ∩ Dj | Ci ∩ Dj does not equal the empty set} is also a partition of A.

If ≡1, ≡2, and ≡ denote the equivalences afforded by P1, P2, and P, describe ≡ in terms of ≡1 and ≡2.

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Sadly I don't even understand what exactly this problem is asking me for. How do I describe ≡ at all? Any help would be very very much appreciated.