Question

What condition renders this true, where S and T are sets?

Note: c means complement.

SU(Tc) = SC ∩ T.

Answer 1

There are no sets S, T for which

`S \cup T^c=S^c\cap T`

holds

Explanation:

Let the set A be

`A=S\cup T^c`

By de De Morgan's Law

`A^c=S^c\cap ((T)^c)^c`

But

`((T)^c)^c=T`

`A^c=S^c\cap T`

We conclude that

`S \cup T^c=S^c\cap T\Rightarrow A=A^c`

which is a contradiction because no set is equal to its complement.