Is the Cartesian product of ( A × B ) c a subset of A...
Is the Cartesian product of a subset of ?
Answer & Explanation
Suppose and . Then the Cartesian product is a subset of the Cartesian product .
We know that if both and are true, which fails if either or or both. Thus,
However, the sets and are not disjoint sets so that the pairs where both elements are not in the corresponding subsets are being double counted. This can be corrected as under:
. Thus is not a subset of On the contrary, is a subset of