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Mathematical formulation to this problem is as follows:
You have an Universal set U with n(U) = 92 elements.
There is a subset F (first letter of the word "Father") with n(F) = 47 elements.
There is another subset M (first letter of the word "Mother") with n(M) = 68 elements.
The part (a) asks about the number of elements n(F and M) of the intersection of these two subsets, F and M.
From elementary set theory, you have THIS EQUATION
92 - 8 = n(F) + n(M) - n(F and M),
where the last term in the equation is your unknown to find.
Substitute the given values n(F) = 47 and n(M) = 58 into this equation
92 - 8 = 47 + 58 - n(F and M).
Then you get the solution
n(F and M) = 47 + 58 - 84 = 31.
31 is the ANSWER to question (a).
Part (a) is solved.
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(b) This question asks, how many elements has the set (F U M) \ (F intersection M).
The sign " \ " symbolizes the difference of the sets.
The number of elements in this set is n(F) + n(M) - 2*n(F and M) = 47 + 68 - 2*31 = 53. ANSWER
(c) This question asks, how many elements has the set F U M.
The number of elements in this set is n(F) + n(M) - n(F and M) = 47 + 68 - 31 = 84. ANSWER
I answered all question, but, probably, omitted some details in my explanations.
I made it CONSCIOUSLY to leave a room for your thoughts.
See the lesson
- Counting elements in sub-sets of a given finite set
in this site.
Let this lesson be your first step in the Elementary Set Theory.
Happy learning (!)
Come again to the forum soon to learn something new (!)
It may happen that after reading my post and my lesson, you will want to learn more about the subject.
Then let me know - I will tell you what to read next.