A proof of De Morgan’s law
1.5
Prove that S ? T = S ? T
by showing that each set is a subset of the other.
1. Suppose x ? S ? T.
I.e. x? S ? T.
Then x?S or x?T.
Hence, x?S or x?T.
This means that x ? S ? T.
Thus, S ? T ? S ? T.
2. Now suppose x ? S ? T.
Then x?S or x?T.
Hence x? S or x?T,
which means that x? S?T.
Therefore, x? S?T.
End of proof
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