Consider P and Q be non-empty families of sets, and consider C subset of P and D subset of Q be chains. Is CxD always chain in PxQ? Write the proof or counterexample.
Consider P be the non-empty family of sets, consider I be non-empty set and consider {Ci} for all i in I be family of chains in P.
1. Is intersection of Ci always a chain in P? Write the proof or the counter example.
2. Is union of Ci always the chain in P? Write the proof or the counter example.