Consider basic modal logic. Recall that $\backslash$alpha $\backslash$beta is an abbreviation for $(\backslash$alpha $->\backslash$beta $)(\backslash$beta $->\backslash$alpha $).$ Using the tableau method, show that the formulas $($i$)$ and $($ii$)$ are valid.

Using the tableau method, show that the formulas $($iii$)$ and $($iv$)$ are not valid.

Use the image to check formulas $($i$),($ii$),($iii$),$ and $($iv$)$

$($i$)1,pvv,q,e$

$($ii$),(p^{{?}^{?}}q)harr(p^{{?}^{?}}q).$

$($iii$)$ diamondp$$diamondp, $e$

$($iv$)(pvvq)(pvvq).$ not valid: