L4 – Set Theory

In a class of 46 students, 22 play football and 26 play volleyball. If 3 students play both games, how many play neither?

In a survey of 50 newspaper readers, 40 read Champion and 30 read Guardian, how many read both papers?

if P = {x:x is odd, −1 < x ≤ 20} and Q is {y:y is prime, −2 < y ≤ 25, find P ∩ Q

From the venn diagram above, the shaded parts represent

Given that A = {1, 5, 7}
B = {3, 9, 12, 15}
C = {2, 4, 6, 8}

Find   \[(A\cup B)\cup C\]

A cinema hall contains a certain number of people. If 22.5%   are children, 47.5% are men and 84 are women, find the number of men in the hall.

In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like both music?

If n(P) = 20 and n(Q) = 30 and n(PuQ) = 40, find the value n(PnQ)

If T = {prime numbers} and M = {odd numbers} are subsets of μ = {x : 0 < x ≤ 10} and x is an integer, find (T′ n M′).

In a school, 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 Mathematics. How many offer Biology but not Mathematics?

The figure below is a Venn diagram showing the elements arranged within sets A,B, and C.
Use the figure to answer this question

What is n(A U B) ?

The figure below is a Venn diagram showing the elements arranged within sets A,B,C,ε.

Use the figure to answer this question

What is n(A U B)^I ?

Four members of a school first eleven cricket team are also members of the first fourteen rugby team. How many boys play for at least one of the two teams?

A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both language. How many students speak neither Hausa nor Igbo?

In a small village of 500 people, 350 speak the local language while 200 speak pidgin English. What percentage of the population speak both.

In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology?

The Venn diagram above shows a class of 40 students with the games they play. How many of the students play two games only?

If the universal set μ = {x : 1 ≤ x ≤ 20} and
A = {y : multiple of 3}
B = |z : odd numbers}
Find A ∩ B

Given
P = {1, 3, 5, 7, 9, 11}
and Q = {2, 4, 6, 8, 1, 12}. Determine the relationship between P and Q

In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither Mathematics nor Physics. How many offer both Mathematics and Physics?

If X = {all the perfect squares less than 40}
Y = {all the odd numbers from 1 to 15}. Find X ∩ Y.

Given T = {even numbers from 1 to 12}

N = {common factors of 6, 8 and 12} Find T n N

In a school of 150 students, 80 offer French while 60 offer Arabic and 20 offer neither. How many students offer both subjects?

Given U = {x: x is a positive integer less than 15} and P = {x: x is even number from 1 to 14}. Find the compliment of P.

If Q is a factor of 18 and T is prime numbers between 2 and 18. What is Q$\cap$T?

X and Y are two sets such that n(X) = 15, n(Y) = 12 and n{X ∩ Y} = 7. Find n{X ∪ Y}

Given that A = {1, 5, 7}
B = {3, 9, 12, 15}
C = {2, 4, 6, 8}
Find (A ∪ B) ∪ C

In a class of 150 students, the sector in a pie chart representing the students offering Physics has angle 12^o. How many students are offering Physics?

A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

The shaded region in the Venn diagram above is