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A bar graph can represent boolean variables over time by using two bars for each time period. One bar would represent the number of times the variable was true during that period, and the other bar would represent the number of times the variable was false. The height of each bar would correspond to the number of occurrences of each value. For example, if the variable was true for 4 out of 8 time periods, the true bar would have a height of 4 and the false bar would have a height of 4. This would provide a visual representation of the frequency of the true and false values over time.