If $(L, \land, \lor, 0, 1)$ is a lattice, and there exists a unary operation ' on $L$ such that
(x \lor x')=1, and
(x \land x')=0
both hold, is the unary operation ' an isomorphism between the semilattices $(L, \land)$ and $(L, \lor)$? If we add the condition that ' is an involution (i. e. $x''=x$), is ' an isomorphism?