Question 1
Given the following Venn diagram where C is the set of people who eat cereal for breakfast and T is the set of people who eat toast for breakfast.
Work out P(C \cap T).
Select the correct answer from the list below:
A: \dfrac{6}{9}
B: \dfrac{1}{10}
C: \dfrac{2}{21}
D: \dfrac{6}{73}
CORRECT ANSWER: D: \dfrac{6}{73}
WORKED SOLUTION:
P(C \cap T) Equals the intersection of C and T.
P(C \cap T)=\dfrac{6}{73}
Level 6
Question 2
Given the following set information, determine the set B.
A\cap B=\{3,4,6,8\}
A\cup B=\{3,4,5,6,7,8,9,10,12,14,16,18\}
A=\{3,4,5,6,7,8,9,10\}
Select the correct answer from the list below:
A: B=\{3,4,6,8,12,14,16,18\}
B: B=\{3,4,6,8\}
C: B=\{3,4,6,8,16,18\}
D: B=\{12,14,16,18\}
CORRECT ANSWER: A: B=\{3,4,6,8,12,14,16,18\}
WORKED SOLUTION:
We will start with the union as our base for B, as this is everything that could possibly be in B:
A\cup B=\{3,4,5,6,7,8,9,10,12,14,16,18\}
The intersection now tells us the bit in the middle, which is everything in A and B.
And now we can fill up A with everything that is left in its set.
And now, everything that is left in the union must be strictly in B.
Finally, we just need to look at everything inside the B circle.
So, we can see that B=\{3,4,6,8,12,14,16,18\}.
Level 6
Question 3
On the Venn diagram below, shade the region represented by B'.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: D: B'
WORKED SOLUTION:
B' mean not B, so everywhere that is not inside of B should be shaded in.
Level 6
Question 4
On the Venn diagram below, shade the region represented A ∪ B.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B: A ∪ B
WORKED SOLUTION:
A ∪ B means A or B, so everywhere inside A and everywhere inside B should be shaded.
Level 6
Question 5
On the Venn diagram below, shade the region represented A ∩ B.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B: A ∩ B'
WORKED SOLUTION:
Level 6
Question 6
On the Venn diagram below, shade the region represented A ∩ B'.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B: A ∩ B'
WORKED SOLUTION:
Level 6
Question 7
On the Venn diagram below, shade the region represented A' ∩ B'.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A: A' ∩ B'
WORKED SOLUTION:
A' ∩ B' means Not A and Not B.
Level 6