$$x\wedge\neg x$$

Question

$$x\wedge\neg x$$

hartnn · Answer

null ?

unklerhaukus · Answer

no solutions?

hartnn · Answer

null set can be treated as a solution....

unklerhaukus · Answer

hmm,

unklerhaukus · Answer

i thought

$$\neg\emptyset=U$$

hartnn · Answer

that is correct, but why did u have to negate null ? to get universal set?

unklerhaukus · Answer

i dont know,
im new to this stuffs

unklerhaukus · Answer

is $x=\emptyset$ a solution 

or does  $x=\emptyset$ mean there are no solutions

unklerhaukus · Answer

@Mikael

anonymous · Answer

There is a third alternative. This expression does not preclude it.

unklerhaukus · Answer

go on,..

anonymous · Answer

http://en.wikipedia.org/wiki/Many-valued_logic $$ \Huge \color{Green} {and \quad it \quad goes\quad free-er!}$$ http://en.wikipedia.org/wiki/Free_logic

unklerhaukus · Answer

?

anonymous · Answer

You have written a logical 1-st order expression
X and NOT-x
in $$ \bf the \quad standard$$  $$ \Huge \color{Green} { \quad\cal BIVALENT\quad Logic} $$
This is equivalent to NO-SOLUTION or empty set of satisfying instances.
But there is a legitimate formal study WITHOUT the law of excluded-third (meaning that in addition to YES or NO there is additional possibility.

I supplied you the beginning of this field -ref