Is the system of connectives $\{\lnot, \leftrightarrow\}$ complete?

Question

If we consider the system$ \{\lnot, \leftrightarrow\}$ can we express all the connectives like $\wedge$, $\vee$ or $\rightarrow$ just by using $\lnot$ and $\leftrightarrow$ ?

Thanks in advance !

Answer 1

With two variables $a,b$, anything you can construct with $\neg$ and $\leftrightarrow$ is true in an even number of the four possible cases. This follows by structural induction. As a consequence, you cannot obtain $a\land b$.