Question 1:
For the following Set notations, which is the correct description?
1(a) A\cap B
ANSWER: Multiple Choice
A: Belonging to both A and B
B: Belonging to A but not B
C: Belonging to A or B or both
D: Not belonging to A or B
Answer: A
Marks = 1
1(b) A' \cup B
ANSWER: Multiple Choice
A: Belonging to B or not belonging to A
B: Not belonging to B but belonging to A
C: Not belonging to A or B
D: Not belonging to A and B
Answer: A
Marks = 1
1(c) If A = even numbers more than 0 and B = prime numbers, what would A\cap B be?
ANSWER: Multiple Choice
A: \{2\}
B: \{2,-2\}
C: \{0,2\}
D:\{-2,0,2\}
Answer: A
Marks = 1
Question 2:
Consider the following Venn diagram.
2(a) Which values are described by A′?
ANSWER: Multiple Choice
A: 1,9,25,49
B: 4,16,36
C: 1,4,9,16,25,36,49
D: 2,6,18,30,34,40
E: 1,2,6,9,18,25,30,34,40,49
Answer: A
Workings:
A‘ is all the values not in A.
Marks = 1
2(b) Which values are described by A\cap B?
ANSWER: Multiple Choice
A: 1,9,25,49
B: 4,16,36
C: 1,4,9,16,25,36,49
D: 2,6,18,30,34,40
E: 1,2,4,6,9,16,18,25,30,34,36,40,49
Answer: B
Workings:
A\bigcap B is the values in A and B.
Marks = 1
2(c) Which values are described by A\cup B?
ANSWER: Multiple Choice
A: 1,9,25,49
B: 4,16,36
C: 1,4,9,16,25,36,49
D: 2,6,18,30,34,40
E: 1,2,6,9,18,25,30,34,40,49
Answer: E
Workings:
A\cup B is all of the numbers in both sets.
Marks = 1
Question 3:
Students were asked about their subjects taken in Year 10.
The options in this case were Biology and Textiles.
Originally, the probability that a student took Biology was \dfrac{7}{20}
A new student joins the group and now the probability is \dfrac{1}{3}.
In both cases, 3 students took neither of the two subjects.
3(a) Select the correct Venn diagram to display the information provided.
ANSWER: Multiple Choice
A: 
B:
C:
D:
Answer: C
Workings:
1 other person joins the group, so the total number of students is now 21.
The probability that a student studies Biology is now \dfrac{7}{21}=\dfrac{1}{3}. This means 7 students study biology, so the number of students that do not study Biology is 21-7=14.
Of the 14 students that do not study Biology, 3 of them do not study Textiles. So the number of students that study Textiles only is 14-3=11.
This is all the information we have to fill the Venn diagram.
Note: although 7 students study Biology, there is not enough information to say whether or not they also study Textiles, so the ‘Biology only’ and ‘Biology and Textiles’ fields must remain blank.
Marks = 2
3(b) Which of the following probabilities would help you fill in the rest of the Venn diagram?
ANSWER: Multiple Choice
A: \text{P(}B\cap T\text{)}
B: \text{P(}B\text{)}
C: \text{P(}B\text{')}
D: \text{P(}T\text{)}
Answer: A
Workings:
\text{P(}B\cap T\text{)} is would give the number in the intersection, i.e. the number of students that study both Biology and Textiles.
Marks = 1
Question 4
Consider the sets A and B.
4(a) Which of the following Venn diagrams displays the shaded region represented by B′?
ANSWER: Multiple Choice
A:
B:
C:
D:
Answer: A
Workings:
B′ is the area not in B, so everything outside of the circle of B should be shaded.
Marks = 1
4(b) Which of the following Venn diagrams displays the shaded region represented by A\cap B′?
ANSWER: Multiple Choice
A:
B:
C:
D:
Answer: A
Workings:
A\cap B′ is the area in A that is not also in B.
Marks = 1
4(c) Which of the following Venn diagrams displays the shaded region represented by (A\cup B)′?
A:
B:
C:
D:
Answer: A
Workings:
A\cup B is the area in A or B. Therefore (A\cup B)‘ is the area in neither A nor B. It is important to consider the brackets in this case.
Marks = 1
Question 5
Consider the sets A and B.
5(a) Which of the following Venn diagrams displays the shaded region represented by A\cup B?
ANSWER: Multiple Choice
A:
B:
C:
D:
Answer: A
Workings:
A\cup B is the region in either A or B.
Marks = 1
5(b) Which of the following Venn diagrams displays the shaded region represented by A\cap B‘?
ANSWER: Multiple Choice
A:
B:
C:
D:
Answer: A
Workings:
A\cap B‘ is the region in A that is not in B.
Marks = 1
Question 6:
Given the information below
A Venn diagram is shown below.
68, 58 and 62 are represented by which of the following sets?
(A\cup B)′
(A\cup B)
(A\cap B)'
(A\cap B)
Workings:
Marks = 3