if You're going to need conditions on the three sets in order to make it false. It's certainly not going to hold for all sets!
Show that is false for all sets A, B and C using direct proof.
I'm not sure how to finish off my proof... can someone please help
If we were to prove that the statement is true then we would need to show that if then and if then
To formalise this we denote the following:
Let P(x) denote the proposition function "" and Q(x) denote the proposition function ""
Thus we need to show that and
Let us first focus on
Because we are using a direct proof let us assume the hypothesis P(x) is true. If we can show that Q(x) is false then the universally quantified statement is false and we have complete our proof.
Since P(x) is assumed to be true then can be interpreted as or .
is only true if:
1. is true and is true
2. is true and is false
3. is false and is true
Now Q(x) is interpreted as and
Now what...?
Do you mean "false for all sets" or "not true for all sets"?
The first is, as Akbeet said, not a true statement so you cannot prove it.
But the second, that there exist some sets for which , is true. A counter example is the simplest way to show that- exhibit one of those sets.