Verify that the Cartesian product is an associative operator—that is, r × (s × t)=(r × s) × t for all relations r, s,and t.
What will be an ideal response?
r × (s × t)=r ×{< s, t >| s ? s, t ? t} = {< r , s, t >| r ? r, s ? s, t ? t}
(r × s) × t = {< r , s >| r ? r, s ? s}×t = {< r , s, t >| r ? r; s ? s; t ? t)
Thus, r × (s × t)=(r × s) × t
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