## SET THEORY – What is a Set?

Set is the collection of well-defined objects or things. It can also be defined as the collection of objects or things that has something in common. In Set Theory, A Set can be represented by a capital letter and its listed members can be enclosed in braces. **( kindly use the comment box below to ask a question).**

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### Questions on Set Theory

- If A is the set of even numbers between 1 and 20, and B is the set of prime numbers between 1 and 20.

(A.) (I) List all the elements of A

(II) List all the elements of B

(B.) Find the following:

- A∩B
- A∪B
- A
^{c}∪B^{c} - A
^{c}∩B^{c} - A∩B
^{c}

- If

A = {1, 4, 7, 10, 13, 16}

B = {3, 5, 7, 9, 11, 13, 15} and

C = {3, 10, 11, 16} Verify that;

- A∪B = B∪A
- (A∪B)∪C = A∪(BC)
- A∪(B∩C) = (A∪B)∩(A∪C)

- Prove the following by:

- Definition and
- Venn diagram

- (A∩B) ∩C = A ∩(B∩C)
- A∪(B∩C) = (A∪B) ∩(A∪C)
- (A∩B)
^{c }= A^{c }∪B^{c} - (A∪B)
^{c }= A^{c }∩B^{c}

- In Sound Foundation High School there are 400 students in the final year, 300 0f them do biology, 150 do physics. How many of them do both subjects?

- In a class of 100 students, 57 offer health science and 60 offer biology. How many of them offer both subjects if 5 of them do not offer any of the two subjects.

- A joint meeting of Mathematicians and Statisticians had 232 members in attendance. If 146 are Mathematicians and 205 are Statisticians, how many of them are both Mathematicians and Statisticians?

- The following list shows the preferences of 1,102 people at the end of the year party organized by the management of the college.

99 like Juju music, 96 like Fuji music, 99 like Afro music, 95 like Juju and Fuji, 94 like Fuji and Afro, 96 like Juju and Afro, 93 like all the three.

How many people like:

- None of the three?
- Juju only.
- Anything but afro.
- Only Fuji.
- Exactly two kinds of music.

- There are 100 students in the LEVEL 3 accounting class. 75 of them passed Business Mathematics while 40 passed in Use of English. How many students passed in both subjects?

- A survey of 80 students’ shows that 60 of them speak Yoruba and 20 speak Hausa, while 8 speak both languages. How many speak neither Yoruba nor Hausa?

- In a school of 120 students, 41 studied Maths, 48 studied Chemistry and 42 studied Physics, 16 studied both Chemistry and Maths, 14 studied Maths and Physics, 18 studied Chemistry and Physics and 9 studied all the three subjects. How many of them studied…

- Exactly one subject.
- At least one subject.
- None of the subjects.

## Other Mathematics Questions

- Co-ordinate Geometry
- Linear Programming
- Permutation and Combination
- Empirical Probability
- Integration & Vector Algebra
- Differentiation

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