Using Set Theory. A ~ Set of Students Studying Math B ~ Set of Students Studying History A ∩B ~ The intersection of sets A and B. (Students who study Math and History). S. 2 Sets are disjoint if their intersection is the empty set Ø. Disjoint Sets.
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e.g. if C is the set of students studying grade 10 history and A is the set of students studying grade 12 math there are no grade 10 history students who study grade 12 math.
B = set of P.E. Students
There are 28 DM students and 25 PE students. 12 are in both. How many students in total are in DM or PE (or both)?
n(A)=28, n(B)=25, n( A∩B )=12
n( A UB) = n( A) + n( B) – n( A∩B )
=28 + 25 – 12
Of the 120 students in a class, 30 speak Chinese, 50 speak Spanish, 75 speak French, 12 speak Spanish and Chinese, 30 speak Spanish and French, and 15 speak Chinese and French. Seven students speak all three languages. How many students speaks none of these languages?
7 speak all 3 elements in either A or B or both
15 speak Chinese and French
30 speak Spanish and French
12 speak Spanish and Chinese
50 speak Spanish
30 speak Chinese
75 Speak French
120 – 105 = 15 don’t speak any.