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Discrete Mathematics | 1st Edition | ISBN: 9781577667308 | Authors: Gary Chartrand, Ping Zhang
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A total of 36 students plan to take at least one of the courses Discrete Mathematics

Chapter 8, Problem 10

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QUESTION:

A total of 36 students plan to take at least one of the courses Discrete Mathematics, Algebra and Calculus during the coming semester. Of these 36 students, it is known that 23 students plan to take Discrete Mathematics, 19 students plan to take Algebra, 18 students plan to take Calculus, 7 students plan to take Discrete Mathematics and Algebra, 9 students plan to take Discrete Mathematics and Calculus and 11 students plan to take Algebra and Calculus. (a) How many students plan to take all three courses? (b) How many students plan to take exactly one of the courses? (c) How many students plan to take exactly two of the courses?

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QUESTION:

A total of 36 students plan to take at least one of the courses Discrete Mathematics, Algebra and Calculus during the coming semester. Of these 36 students, it is known that 23 students plan to take Discrete Mathematics, 19 students plan to take Algebra, 18 students plan to take Calculus, 7 students plan to take Discrete Mathematics and Algebra, 9 students plan to take Discrete Mathematics and Calculus and 11 students plan to take Algebra and Calculus. (a) How many students plan to take all three courses? (b) How many students plan to take exactly one of the courses? (c) How many students plan to take exactly two of the courses?

ANSWER:

Step 1 of 4

Given

 Total 36 students plan to take at least one of the courses Discrete Mathematics (D), Algebra( A), Calculus ( C) .

Suppose that let x be the number  who take all the courses.

From the diagram,

Number who takes (D) only are

Number who takes ( A) only are

Number who takes Calculus ( C)

Adding up all regions of the venn diagram should 36

 

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