Let us jump straight to the problems to understand the solution methodology.
Example:
Let A = {0, 1, 3, 5}, B = {5, 6, 1, 3, 9} and C = {0, 1, 2, 3, 9, 13}.
Then, 
:
[1] {0, 1, 2, 3, 9, 13}
[2] {0, 1, 2, 3, 5, 9, 13}
[3] {0, 1, 3}
[4] {1, 3}
Solution:
Therefore, the correct option is [2].
Example:
How many numbers are there between 1 and 100 that are not divisible by 2, 3 and 5?
[1] 26
[2] 36
[3] 40
[4] 68
Solution:
Let us draw a Venn Diagram with the information as provided above.
therefore numbers divisible by 2, 3 and 5 = 27 + 13 + 3 + 7 + 14 + 3 + 7 = 74
therefore numbers not divisible by 2, 3 and 5 = 100 – 74 = 26
Therefore, the correct option is [1].
Refer to the data below and answer the questions that follow.
A school has 63 students studying Physics, Chemistry and Biology. 33 study Physics, 25 Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study Biology and Chemistry while 8 study both Physics and Biology. Equal numbers study all three subjects as those who learn none of the three.
Example:
How many study all the three subjects?
[1] 2
[2] 3
[3] 5
[4] 7
Solution:
Let us draw a Venn diagram.
From the diagram, 3 students study all the three subjects.
Therefore, the correct option is [2].
Example:
How many study only one of the three subjects?
[1] 21
[2] 30
[3] 39
[4] 42
Solution:
33 + 25 –(19 – x) + 9 – x +26 –(17 – x) = 63 – x
33 + 25 – 19 + x + 9 – x + 26 – 17 + x = 63 – x
57 + x = 63 – x
Now, we have18 + 9 + 12 = 39
Therefore, the correct option is [2].
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