MCQ Questions

Question No. 1

List all the elements of the following sets.

Answer :

a) days of the week

b) factors of 24

c) the first six multiples of 4

Question No. 2

State a rule that describes the following lists.

Answer :

a) 1, 3, 5, 7, 9, 11

b) 2, 3, 5, 7, 11

c) Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune

Question No. 3

The set P = {4, 6, 9} is given.

Answer :

a) Write down the cardinality of set P.

b) Write down all the subsets of P.

c) Is P a finite or infinite set?

Question No. 4

Complete each of the following by writing one of these symbols: ∈ or ∉.

Answer :

a) 18 ___ {prime numbers}

b) 91 ___ {multiples of 7}

c) Igbo ___ {languages spoken in Korea}

d) 144 ___ {square numbers}

Question No. 5

Give ten examples of sets. Write each set in set notation.

Answer :

Question No. 6

Write down the cardinal number of each of these sets: A = {prime numbers from 1 to 10}, B = {teachers who teach your class}, C = {boys in your class}, D = {odd numbers from 1 to 1000}, E = {grains of sand in the Sahara desert}, F = {x: x is a factor of 12}, G = {goat, cat, dog, sheep, cow, horse}.

Answer :

Question No. 7

State whether these sets are finite or infinite: A = {girls in your class}, B = {multiples of 3 from 1 to 50}, C = {2, 4, 6, 8, …}, D = {x: x is the number of countries in the world}, E = {x: x is the number of states in Nigeria}, F = {x: x is a fraction between 1 and 2}.

Answer :

Question No. 8

Which of these sets are empty, which are singletons, which are equal, and which are equivalent? A = {prime numbers divisible by 7}, B = {odd numbers divisible by 2}, C = {1, 2, 3, 4}, D = {the first four multiples of 5}, E = {p, q, r, s}, F = {20, 15, 10, 5}.

Answer :

Question No. 9

Consider the following sets: A = {prime numbers}, B = {even numbers}, C = {odd numbers}, D = {multiples of 3}. Which two sets are disjoint?

Answer :

Question No. 10

Fill in the correct relation sign (⊂, ⊃ or ⊄) in the blank spaces.

Answer :

a) {2, 4, 6, 8} ___ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

b) {pawpaws, bananas, mangoes} ___ {animals}

c) {fruits} ___ {pawpaws, bananas, mangoes}

d) {2, 3, 5, 7} ___ {2, 3, 5, 6}

e) { } ___ {2, 4, 6, 8, 10}

f) {1, 2, 3, 4, 5} ___ {2, 4}

g) {animals} ___ {domestic animals}

Question No. 11

Find the power set of these sets and write down the cardinality of this power set.

Answer :

a) P = { }

b) Q = {1}

c) R = {a, b}

d) S = {a, b, c}

e) T = {2, 4, 6, 8}

Question No. 12

List all the possible subsets of each of the following sets.

Answer :

a) {a, b}

b) {a, b, c}

c) {a, b, c, d}

d) {a, b, c, d, e}

Question No. 13

Complete the table below.

Answer :

Number of elements in a set: 0, 1, 2, 3, 4, 5 Number of subsets: ___

Question No. 14

Generalise your findings: The number of subsets in a set P with n elements is ___.

Answer :

Question No. 15

Given: A = {4, 5, 8, 16}, B = {2, 4, 8, 16} and C = {7, 9, 15}. List all the elements in each of the following.

Answer :

a) A ∪ B

b) B ∪ C

c) A ∪ C

d) A ∪ B ∪ C

Question No. 16

Given: X = {1.5, 2, 2.5, 3, 3.5}, Y = {3, 3.5, 4, 4.5, 5} and Z = {4.5, 5, 5.5, 6, 6.5}. List all the elements in each of the following.

Answer :

a) X ∪ Y

b) X ∪ Z

c) Y ∪ Z

d) X ∪ Y ∪ Z

Question No. 17

Given: P = {3, 7, 21, 147}, Q = {2, 4, 8, 32} and R = {1, 3, 5, 15, 65}. List all the elements in each of the following.

Answer :

a) P ∪ R

b) R ∪ Q

c) Q ∪ P

d) R ∪ P ∪ Q

Question No. 18

Given: A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8} and C = {1, 2, 4, 8, 16}. List all the elements in each of the following.

Answer :

a) A ∩ B

b) B ∩ C

c) A ∩ C

d) A ∩ B ∩ C

Question No. 19

Given: X = {−5, −4, −3, −2, −1}, Y = {−11, −9, −7, −5} and Z = {−9, −3, −1}. List all the elements in each of the following.

Answer :

a) X ∩ Y

b) X ∩ Z

c) Y ∩ Z

d) X ∩ Y ∩ Z

Question No. 20

Given: P = {a, p, p, l, e}, Q = {m, a, n, g, o} and R = {o, r, a, n, g, e}. List all the elements in each of the following.

Answer :

a) P ∩ R

b) R ∩ Q

c) Q ∩ P

d) R ∩ P ∩ Q

Question No. 21

Given the sets V = {all even numbers}, O = {all odd numbers} and P = {all prime numbers}, say whether the following pairs of sets are disjoint or not. If the sets are not disjoint, give one example of an element of the intersection of the sets.

Answer :

a) V and O

b) V and P

c) O and P

Question No. 22

In the Venn diagram: B = {students who take Biology}, M = {students who take Mathematics}, P = {students who take Physics}.

Answer :

a) How many students take Biology?

b) How many students take either Mathematics or Physics?

c) How many students take only Physics?

d) How many students take all three subjects?

e) How many students take either Biology or Mathematics or Physics?

Question No. 23

All the 250 students in a class learn German or Spanish or both. Given that 144 students learn German and 128 learn Spanish, how many students learn both languages?

Answer :

Question No. 24

In a class of 70 boys, each boy takes part in either football or basketball or both. Given that 40 boys play football and 8 play both football and basketball, find how many boys play basketball.

Answer :

Question No. 25

In a household survey, it was discovered that 85 of the homes visited had televisions, 128 had radios and 32 had both a television and a radio. How many households were there in the survey?

Answer :

Question No. 26

Given that n(X) = 18, n(Y) = 36 and n(X ∪ Y) = 50, find n(X ∩ Y).

Answer :

Question No. 27

Given that n(P) = 28, n(Q) = 36 and n(P ∩ Q) = 8, find n(P ∪ Q).

Answer :

Question No. 28

Given that n(S) = 18, n(S ∪ T) = 40 and n(S ∩ T) = 5, find n(T).

Answer :

Question No. 29

Given that n(A) = 118, n(B) = 98, n(C) = 94, n(A ∩ B) = 42, n(B ∩ C) = 24, n(A ∩ C) = 34 and n(A ∩ B ∩ C) = 8, find n(A ∪ B ∪ C).

Answer :

Question No. 30

The pets of five families are represented in set form, as follows: The Ozobia family: {dogs, goats, sheep} The Mordi family: {cats, chickens} The Ifedi family: {cats, dogs, rabbits}. List the universal set for the pets that these families own.

Answer :

Question No. 31

A teacher wrote down the birthdays of all the students in her class.

Answer :

a) List the universal set for the months of the birthdays

b) List the universal set for the days of the months of the birthdays

Question No. 32

Some of the languages spoken in Nigeria are Igbo, Yoruba, Fulfulde, Kanuri, Hausa and Ibibio.

Answer :

a) List the universal set for this situation

b) How many subsets are there in the universal set in question a)?

Question No. 33

Write down n(ξ) for each of the following situations.

Answer :

a) There are 39 boys and 28 girls in a class

b) A box of shapes contains triangles, circles, squares, rectangles, parallelograms, kites, pentagons and hexagons

Question No. 34

Consider these sets of numbers, and identify the universal set: J = {the first six prime numbers}, L = {the first five multiples of 3}, M = {all the factors of 16}.

Answer :

Question No. 35

Given the following sets: ξ = {a, b, c, e, f, h, i, k, m, o, p, r, s, t, w}, C = {c, h, r, i, s, t, o, p, h, e, r} and T = {t, a, p, i, w, a, h}.

Answer :

a) Draw the Venn diagram of this situation.

b) List the elements in C ∩ T.

c) List the elements in C ∪ T.

Question No. 36

Given the following sets: ξ = {integers between 1 and 29}, X = {multiples of 2 between 1 and 29}, Y = {prime numbers between 1 and 29} and Z = {multiples of 3 between 1 and 29}.

Answer :

a) Draw the Venn diagram of this situation.

b) List the elements in X ∩ Y.

c) List the elements in Y ∩ Z.

Question No. 37

In a school of 272 students, 70 are members of the Science Society. 30 belong to both the Science and Debating Societies. 142 belong to neither society. How many students belong to the Debating Society?

Answer :

Question No. 38

A party of 120 tourists planned to visit Nigeria, Cameroon and Benin. 68 tourists visited Cameroon and 70 tourists visited Benin. 40 tourists visited Nigeria and Cameroon, 46 tourists visited Nigeria and Benin and 37 tourists visited Benin and Cameroon. 25 tourists visited all three countries. How many tourists visited Nigeria altogether?

Answer :

Question No. 39

A teacher is handing out textbooks to a SS1 class. Every student in the class gets a Maths book. The teacher hands out 48 Maths books, 22 Geography textbooks, 17 History textbooks and 18 Science textbooks. 7 students take History and Geography, 9 students take Science and Geography and 5 students take History and Science. 9 students do not take Geography, History or Science. How many students take all four subjects? (Hint: View the Maths students as the universal set, because every student is al

Answer :

Question No. 40

A trader reported to a manufacturer on the faults that occurred in 45 radios. He reported the following findings: Fault A occurred 25 times. Fault B occurred 20 times. Fault C occurred 22 times. Faults A and B occurred 4 times. Faults A and C occurred 3 times. Faults B and C occurred 10 times. Only once did all three faults occur in a single radio. Use a Venn diagram to explain why the manufacturer did not believe the trader’s report.

Answer :

Question No. 41

If ξ = {a, b, c, d, e, f, g, h, i}, give the complement of each of the following.

Answer :

e) ξ

a) {a, b, d}

b) {c, d, e, i}

c) {a, c, e, g, i}

d) { }

Question No. 42

If ξ = {all positive integers}, describe the complement of each of the following in words.

Answer :

a) {all positive even numbers}

b) {all positive rational integers}

c) {all prime numbers}

d) {1, 2, 3, 4, 5, 6, 7, 8, 9}

Question No. 43

If ξ = {all positive multiples of 5} and A = {all positive multiples of 10}, describe A' in words.

Answer :

Question No. 44

Given: A = {all prime factors of 30} and B = {all prime factors of 105}, and ξ = A ∪ B.

Answer :

a) List the elements of A and of B.

b) List the elements of A' and of B'.

c) Draw a Venn diagram to illustrate the relation between A and B, labeling each component of the diagram.

d) List the elements of A ∩ B and of A ∪ B.

e) Find the HCF and LCM of 30 and 105.

f) If C = {all prime factors of the HCF of 30 and 105}, and D = {all prime factors of the LCM of 30 and 105}, list the elements of C and D.

g) What do you notice about the sets A ∩ B, A ∪ B, C and D?

Question No. 45

Given: ξ = {prime factors less than 20}, A = {prime factors of 252}, and B = {prime factors of 1716}.

Answer :

a) List the elements of ξ, A and B.

b) Draw a Venn diagram to illustrate the relation between ξ, A and B, marking each component of the diagram.

c) List the elements of A ∩ B, A ∪ B, (A ∩ B)', (A ∪ B)', A' ∩ B', A' ∪ B'. What do you notice?

d) Find the HCF and LCM of 252 and 1716.

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