To answer the question, let's take it step by step:
(a) Represent the given information in set notation.
Let's define the following sets:
- Let \( M \) be the set of students who passed Maths only.
- Let \( S \) be the set of students who passed Science.
- Let \( F \) be the set of students who failed both subjects.
Then we can represent the given information in set notation as follows:
- \( M \) = 45% of total students passed Maths only.
- \( S \) includes all students that passed Science; however, the percentage is not directly given.
- \( F \) = 8% of total students failed both subjects.
(b) Show the given information in a Venn diagram.
A Venn diagram would depict two overlapping circles (one for set \( M \) and one for set \( S \)) with the percentage of students failing both subjects (representing set \( F \)) outside these two circles. Since we can't visualize a Venn diagram in text, I'll describe what it should look like:
1. Draw two intersecting circles, labeling one circle 'Maths' and the other 'Science'.
2. In the 'Maths' circle, indicate the portion of students who passed only Maths (i.e., set \( M \), which is 45%).
3. In the intersection of the two circles, write the percentage that represents the students who passed both subjects, which we will need to calculate since it isn't provided.
4. Outside both circles but within a rectangle that encompasses the circles (representing all students), indicate 8% who failed both subjects (set \( F \)).
5. The remaining area in the 'Science' circle will be the students who passed only Science, which we need to calculate.
(c) Find the total number of students.
Given that 188 students passed Science and the percentage of students passing Science (or having passed Science or Maths) is not directly given, we'll assume that the 40% refers to the students who passed Science, either alone or in addition to Maths, given that the other possibility (Science only) cannot be derived from the given information.
Then, the proportion of students who passed Science (\( S \)) to the total number of students can be written as:
\[ \frac{188}{\text{Total number of students}} = 40\% \]
To find the total number of students, we solve for the total:
\[ \text{Total number of students} = \frac{188}{0.40} \]
\[ \text{Total number of students} = 470 \]
There are 470 students in total who took the examination.
(d) What percentage of the total students are there in the examination?
This question seems to ask for the proportion of students who took the exam with respect to some other group. Since we are only provided the exact count of students who took the examination, the percentage with respect to itself is 100%. Without additional context or a comparative group, this is the most logical answer.
So, 100% of the total students took the examination because 'total students' refers to all the students who took the examination.
