if you’re good with set theory diagrams and word problems for math 30 please help out with questions 23, 24, 25, and 26

23.Option B is correct

24. Option C is correct

25. Option A is correct

26. Option A is correct

Explanation:

23. The number of students participated in all three activities:

N= 30-(5+1+2+3+4+2+2) = 30-19=11

=> Option B is correct

24.

A. n(C⋂D⋂F)=2, not 8 (as shown in picture) => incorrect

B. n(D⋂F⋂C)=2, not 0 (as shown in picture) => incorrect

C. n(D⋂F⋂C)=2, => correct

D n(D⋂F⋂C)'= 7+6+1+9+5+12+0=40, not 7 => incorrect.

25.

According to the picture and the given data:

n(F⋂B)= 3

n(F⋂B) = ii = 3  

=> There is no error in ii (Option B is incorrect)

n(F) = 12

n(F) = i + ii = 12 + 3 = 15

=> error in i (ii is correct), i should be equal to n(F) - ii = 12 - 3 = 9

=> Option A is correct  ( (there is error in i)

n(B) = 7

n(B) = ii + iii = 3 + 4 = 7

=> no error in iii (Option C is incorrect)

n(F⋃B)' = n(F+B-(F⋂B))'=20-(12+7-3)=4

n(F⋃B)' = iv = 4

=> no error in iv (Option D is incorrect)

26.

B, (A⋂B⋂C) = {2}, not empty => incorrect

C, (A⋂B⋂C) = {3}, not empty => incorrect

D, (A⋂B⋂C) = {4, 3}, not empty => incorrect

=> Option A is correct

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