Math

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105 students were asked if they liked soccer, rugby, or football. 4 liked only rugby, 40 liked rugby, 12 liked only rugby and football, 63 did not like football, 21 didn't like any, 16 liked only soccer and football, 60 liked soccer. How many liked only football? How many liked all three sports? How many liked football and rugby? How many liked football or rugby? I drew a Venn Diagram with 3 circles. When I label the regions without information with letters to solve for the information, I labeled the soccer only with a, the football only with b, the soccer and rugby intersection with c. How do I find the intersection of all 3? Should it be c+d or d-c or just d?

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