10 points are chosen on a plane. Every possible pair of
points is joined by a line and the midpoint of the line is
marked with red colour. What is the minimum possible number
points on the plane which have been marked with red colour?
Use Venn diagrams to answer each of the following
questions. You must show your Venn diagram for each
problem. 1. A survey of 80 sophomores at a certain
western college showed the following:
36 take English ,32 take history
32 take political science
16 take history and English
16 take political science and history ,14 take political
science and English
6 take all three
How many students:
a) take English and neither of the
other two? ____________
b) Take none of the three
c) take history, but neither of
the other two? ____________
d) take political science and history but not English?
e) do not take political science?