I am stumped on these;
The "catch" to these problems which makes it harder is that you are not allowed to use the QN(Quantifier Negation) rule for any of them, since what you're doing is proving the QN rules.
(where "E" is the existential quantifier and "=" is the biconditional sign)
1. (x)~Fx = ~(Ex)Fx
2. (Ex)~Fx = ~(x)Fx
3. ~(Ex)Fx = (x)~Fx
4. ~(x)Fx = (Ex)~Fx
5. (x)~Fx therefore ~(Ex)Fx
6. (Ex)~Fx therefore ~(x)Fx
7 ~(Ex)Fx therefore (x)~Fx
The "catch" to these problems which makes it harder is that you are not allowed to use the QN(Quantifier Negation) rule for any of them, since what you're doing is proving the QN rules.
(where "E" is the existential quantifier and "=" is the biconditional sign)
1. (x)~Fx = ~(Ex)Fx
2. (Ex)~Fx = ~(x)Fx
3. ~(Ex)Fx = (x)~Fx
4. ~(x)Fx = (Ex)~Fx
5. (x)~Fx therefore ~(Ex)Fx
6. (Ex)~Fx therefore ~(x)Fx
7 ~(Ex)Fx therefore (x)~Fx