DynamicModule[{},
Dynamic[Column[{Button["Again",
expr=RandomChoice@{"P AND NOT Q","P AND NOT Q AND R","P AND NOT Q AND R OR P "};
g=WolframAlpha[expr,"PodCells"];],

g[[6]],
g[[7]]
}],SynchronousUpdating->False]
,

Initialization:>(expr=RandomChoice@{"P AND NOT Q","P AND NOT Q AND R","P AND NOT Q AND R OR P "};g=WolframAlpha[expr,"PodCells"];)
]