Let G be a group acting on a set X$.$ Then there is an induced $($diagonal$)$ action of G over X $\backslash$times X defined by g$($x$,$y$)=($gx$,$gy$).$ We say that the action of G on X is doubly transitive if the induced diagonal action has exactly two orbits.

Show that a doubly transitive action is transitive.$($Hint: Observe that the diagonal action fixes the diagonal, so it is clear which are the two orbits$).$