Question

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

Answer 1

Answer:

There are no sets S, T for which

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

holds

Step-by-step 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.