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Principle of inclusion vs exclusion12/28/2023 ![]() ![]() Having it, we can calculate the number of elements in the union of the three subsets (F U V U X). Of them, 600/4 = 150 elements are divisible by 4 (subset F, from the word Four) Ħ00/5 = 120 elements are divisible by 5 (subset V, from the word fiVe) Ħ00/6 = 100 elements are divisible by 6 (subset X, from the word siX).Ħ00/(4*5) = 30 elements divisible by 4 and by 5 (intersection (F and V) ) Ħ00/(4*6) = 25 elements divisible by 4 and by 6 (intersection (F and X) ) Ħ00/(5*6) = 20 elements divisible by 5 and by 6 (intersection (V and X) ).Ħ00/(3*4*5) = 10 elements divisible by 4, 5 and 6 (intersection (F and V and X) ). We have a universal set U of 600 elements (integer numbers from 1 to 600 inclusive). Problem 3Find the number of positive integers between 1 and 600 inclusive that are not divisible by 4 or 5 or 6. There are 110 numbers between 1 and 300 (inclusive) that are divisible by at least one of three numbers 4, 6 and/or 15. = substitute the obtained numbers from above = ![]() N(F U X U N) = n(F) + n(X) + n(N) - n(F and X) - n(F and N) - n(X and N) + n(F and X and N) = Use the formula for the number of elements in the union of any 3 subsets The problems asks about the number of elements in the union of the three subsets (F U X U N). Of them, we have these in-pair intersectionsģ00/(4*3) = 25 elements divisible by 4 and by 6 (intersection (F and X) ) ģ00/(4*15) = 5 elements divisible by 4 and by 15 (intersection (F and N) ) ģ00/(6*5) = 10 elements divisible by 6 and by 15 (intersection (X and N) ).ģ00/(4*3*5) = 5 elements divisible by 4, 6 and 15 (intersection (F and X and N) ). Of them, 300/4 = 75 elements are divisible by 4 (subset F, from the word Four) ģ00/6 = 50 elements are divisible by 6 (subset X, from the word siX) ģ00/15 = 20 elements are divisible by 15 (subset N, from the word fifteeN). We have a universal set U of 300 elements (integer numbers from 1 to 300). Problem 2How many integer numbers in the range 1 - 300 are divisible by at least one of the integers 4, 6 and 15. The number of those who passed at least one subject is/was 40. Now substitute all given numbers and obtain the ANSWER Or, in simple terms, you want to determine the number of students who passed at least one subject. (passed French) U (passed Physics) U (passed Math) You want to find the number of students in the union set How many students passed one or more of the subjects? Some students were more successful than others: 32 passed French, 27 passed Physics, 33 passed Mathematics Ģ6 passed French and Math, 26 passed Physics and Math, 21 passed French and Physics, and 21 passed French, Math and Physics. Problem 1There is a group of 48 students enrolled in Mathematics, French and Physics.
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