In a survey, 50 shepherds were asked to state if they have sheep and cattle.
28 shepherds have sheep (S), 35 have cattle (C) and 7 have no animals.
The Venn diagram shows part of the information

(a) Find the number of shepherds who have sheep only.
(b) In the diagram, shade the region defined by ( S′ ∩ C′ ).

The Venn diagram shows sets P and Q.

(a) Use set notation to describe the shaded region.
(b) ℰ = { 1,2,3,…,15 }
P = { multiples of 3 }
Q = { prime numbers }
List the elements of:
(i) P∩Q
(ii) P∪Q

Ε = { 2,3,4,5,6,7,8,9,10 }
A = { x : x is an even number }
B = { x : x is a factor of 10 }
(a) List the elements of set:
(i) A
(ii) A′ ∩ B
(b) Find n ( A ∪ B ).

In a survey, 45 students were asked if they use Whatsapp (W) or Facebook (F) as their social media.
The Venn diagram represents part of the information.

(a) Find:
(i) The total number of students who use only one social media,

(ii) The number of students who use neither Whatsapp nor Facebook.

(b) Find:
(i) $n(W\cap F)$,

(ii) $n(W\cap F)$,

(c) Describe in words the set $(W^{\prime }\cap F)$.

In a class of 55 students, 20 are members of Science club (S), and some are members of English club (E).
The other information is shown in the Venn diagram.

(a) Complete the Venn diagram.

(b) Find the number of students who are members of:
(i) Science club but not English club,

(ii) English club.

(c) Find $n(E\cap S)$.

(d) Describe, in words, the set $S^{\prime }\cap E$.

(e) Find the probability that a student chosen at random from the class is a member of:
(i) Neither English club nor Science club,

(ii) Exactly one club.

(f) Five more students in the class join Science club.

Given that $n\left(E\right)=150$, $n\left(A\right)=75$ and $n\left(B\right)=35$.

(a) Find the value of:
(i) x,

(ii) y.

(b) Find:
(i) $n(A\cup B)$,

(ii) $n(A^{\prime }\cup B)$.

A teacher asks 40 students whether they like Apples (A) or Bananas (B). 18 students like apples only, 7 like bananas only and 5 like neither.

(a) Find the value of x.

(b) Write the value of $n(A\cap B^{\prime })$.

(c) Describe the set $n(A\cap B)$ in words.

(d) Use set notation to represent the number of students who like one type of fruit only.

(e) Write in its simplest form, the ratio of number of students who like apples only to the total number of students.

The shaded area in the example diagram below shows the set $A\cap C\cap B^{\prime }$.


Write down the set notation represented by the shaded area in each diagram below.