a. Find the number of students who are taking all three mathematics subjects. b. Fill in the correct number of students in each of the eight regions of the Venn diagram. c. Determine the number of students who are not taking any of the three mathematics subjects? d. How many students are taking Algebra as their only mathematics subject? e. How many students were taking Calculus and Trigonometry but not Algebra?

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A: n(A¯∩B)=n(A¯)+n(B)-n(A¯∪B)From figuren(A¯)=34+26=60n(B)=45+34=79n(A¯∪B)=34+26+45=105

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A: Solution : The complete solution of both the questions is given below in the attachment file.

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A: Given, nA=23nB=15nA∪B=30nA'=10 So, the formula for nA∪B is, nA∩B=nA+nB-nA∪B

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A: To draw the region

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.