I see no direct link between the two, but I would think that the child should be aware that what's on the TV is not real, only fiction (goes for news also

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Much like Sir Krustin said playing cops and robbers, army men etc... is just as violent as TV, just not as graphic. You need to know when to draw the line as to what is acceptable and what is not. as pretty much every show including cartoons are violent, some cartoons excessively.
Daffy Duck teaches us you CAN get shot in the face with a shotgun and be perfectly, okay.