Review the basics of Venn diagrams

You will have encountered Venn diagrams somewhere along your journey of education. These are visual illustrations that show relationships between a collection of sets. While interpreting and/or drawing Venn diagrams are generally not too difficult, it may have been a while since you’ve last seen one. So let’s quickly go over the basics again, using a simple two-set Venn diagram.

In the Venn diagram below, we have two different sets of students - those playing Australian football (set A) and those playing basketball (set B).

The image on the left shows a new set that contains all elements from either set A and set B (i.e. students who play Australian football, basketball, or both). This is known as A union B, or A ∪ B.

The image on the right shows a new set that contains elements that are in both A and B (i.e. the students who play both Australian football and basketball). This is known as A intersect B or A ∩ B. As you can see, A + B = (A ∪ B) - (A ∩ B).

Using these symbols (∪ and ∩) in your workings makes it much easier to keep track of various information presented to you. This is particularly important since you will be dealing with more complicated Venn diagrams with multiple sets in the Decision Making section of the real UCAT exam.

Venn diagram questions may be asked in two different ways

In the first type of questions, you will be asked to interpret a given Venn diagram and work out the value of a certain part of the diagram. In the second type of questions, you will be asked to choose the Venn diagram that best represents given information or conditions.

Even if you feel confident in tackling Venn diagrams, make sure to spend plenty of time practicing both types of questions to avoid any surprises.

Your goal is the answer, not perfection

When you deal with a complex Venn diagram with multiple sets, it is easy to get carried away in working out the value of all sets and intersections. Remember your goal is to arrive at the answer, not aiming for perfection and working out every single detail.

To avoid making this mistake and losing precious time, read the question very carefully and keep asking yourself what it is that you are trying to answer.

Make good use of the whiteboard

In a previous blog article, we’ve encouraged you to work on improving your mental maths skills to solve questions more quickly in the Quantitative Reasoning section.

However, when working on the Venn diagram questions, relying on mental maths skills and short term memory has its limits. Therefore, we advise you to make notes and draw diagrams on the provided whiteboard to minimise confusion and errors for these types of questions. Remember, you have over a minute per question for the Decision Making section.

Medify’s UCAT Online Course contains many practice questions for all four sections and question types, including those related to Venn diagrams. Head over now to get plenty of practice and for more detailed tips.