Let X be a set and let P={A(n)| n is and element of I} be a partition of X. Also, for each n in I let Q(n)= {B(m)| m is an element of J(n)} be a partition of A(n). Prove that {Q(n)| n is an element of I} is a partition of X.
Let X be a set and let P={A(n)| n is and element of I} be a partition of X. Also, for each n in I let Q(n)= {B(m)| m is an element of J(n)} be a partition of A(n). Prove that {Q(n)| n is an element of I} is a partition of X.
I think you need to define terms better before anyone can help you out. What does A(n) signify? What is I? What is J(n)? B(m)? And it also seems you meant to write P(n) instead of P near the beginning.
I think that what he wants to show is that partitioning the parts of a partition yields a new partition.
It's pretty clear from the definition of a partition, applied twice! Each element will be in one and only one sub-part.