Answer:
There are no sets S, T for which
[tex]S \cup T^c=S^c\cap T[/tex]
holds
Step-by-step explanation:
Let the set A be
[tex]A=S\cup T^c[/tex]
By de De Morgan's Law
[tex]A^c=S^c\cap ((T)^c)^c[/tex]
But
[tex]((T)^c)^c=T[/tex]
[tex]A^c=S^c\cap T[/tex]
We conclude that
[tex]S \cup T^c=S^c\cap T\Rightarrow A=A^c[/tex]
which is a contradiction because no set is equal to its complement.
