I have a relation $PC$, defined as:
$$\textbf{PC} = \matrix{model & speed & ram & hd & price \cr 1001 & 2.66 & 1024 & 250 & 2114 \cr 1002 & 2.62 & 1024 & 300 & 800 \cr 1003 & 3.24 & 2048 & 250 & 2570 \cr 1004 & 3.11 & 4096 & 100 & 1100 \cr 1005 & 3.20 & 2048 & 80 & 2400 \cr 1006 & 3.00 & 2048 & 100 & 2570 \cr}$$
I want to isolate $hd$'s that have sizes that exist more than once -- i.e. duplicates. How can I do this using operators such as projection ( $\pi$ )?
So far, I've thought of doing a procedure such as this:
$$A := \pi_{hd}(PC)$$ $$B := \pi_{hd}(PC)$$ $$\pi_{A}(\sigma_{A=B} (A \times B)) - \pi_{hd}(PC)$$
Which I'm hoping would give me the column:
$$\matrix{hd \cr 250 \cr 100 \cr}$$
But I know that projection removes duplicates so I doubt this is right.
Can Anyone point me in the right direction?