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- WELCOME TO A LESSON ON SOLVING PROBLEMS USING VENN DIAGRAMS. LET'S TAKE A LOOK AT OUR FIRST EXAMPLE. 150 COLLEGE FRESHMEN WERE INTERVIEWED. SO THESE STUDENTS MAKE UP OUR UNIVERSAL SET FOR THIS EXAMPLE. 85 WERE REGISTERED FOR A MATH CLASS, 70 WERE REGISTERED FOR AN ENGLISH CLASS, AND 50 WERE REGISTERED FOR BOTH A MATH AND ENGLISH CLASS. THE SET UP THIS VENN DIAGRAM, WE'RE GOING TO WORK OUR WAY BACKWARDS, SO WE'LL START WITH THIS INFORMATION HERE AND WORK OUR WAY UPWARDS. SO 50 WERE REGISTERED FOR BOTH MATH AND ENGLISH. THERE ARE 50 STUDENTS IN THIS REGION HERE WHERE MATH AND ENGLISH OVERLAP. NEXT WE'RE TOLD THAT 70 WERE REGISTERED FOR AN ENGLISH CLASS. AND NOTICE THAT OF THESE 70, 50 OF THEM WERE ALSO TAKING MATH. SO 70 - 50 = 20 STUDENTS TAKING ONLY ENGLISH. SO WHEN IT SAYS 70 WERE REGISTERED FOR ENGLISH, WE HAVE TO ALSO COUNT THOSE TAKING ENGLISH AND MATH, OR THESE 50 HERE. AND THEN 85 WERE REGISTERED FOR A MATH CLASS. AGAIN, 50 OF THE 85 WERE ALREADY ACCOUNTED FOR

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