\begin{center}
\begin{forest}
for tree={circle, draw,
            minimum size=2em,
            inner sep=0pt,
            s sep=2mm,
            l sep=1mm}   
	[$\land$, name=and, label={$T$}
		[$\lor$, name=or, edge label={node[midway,left]{$T$}}
			[$p$, name=p_one, edge label={node[midway,left]{$F$}}]
			[$\imp$, name=imp_one, edge label={node[midway,right]{$T$}}
			    [$\lnot$, name=not_one, edge label={node[midway,left]{$F$}}
                    [$q$, name=q, edge label={node[midway,left]{$T$}}]			    
			    ]
			    [$r$, name=r_one, edge label={node[midway,right]{$T$}}]
			]	
		]		
		[$\imp$, name=imp_two, edge label={node[midway,right]{$T$}}
			[$\lnot$, name=not_two, edge label={node[midway,left]{$F$}}
                [$r$, name=r_two, edge label={node[midway,left]{$T$}}]
			]
			[$p$, name=p_two, edge label={node[midway,right]{$F$}}]
		]		
	]
\end{forest}
\end{center}