Logic and Venn Diagrams for CBEST Exam Study Guide (page 2)

Venn Diagrams

Venn diagrams provide a way to visualize groups in relationship to each other. Words such as some, all, and none commonly appear in these types of questions.

In Venn diagram problems, you are given two or more categories of objects. First, draw a circle representing one of the categories. Second, draw another circle representing the other category. Draw the second circle according to these rules:

1. If the question says that ALL of a category is the second category, place the second circle around the first.

Example: All pigs (p) are animals (a).



 

2. If the question says that SOME of a category is the second category, place the second circle so that it cuts through (overlaps) the first circle.

Example: Some parrots (p) are talking birds (t).



 

3. If the question says NO, meaning that none of the first category is in the second category, make the second circle completely separate from the first.

Example: No cats (c) are fish (f).



 

Sample Venn Diagram Question

3. All bipeds (B) are two headed (TH).Which diagram shows the relationship between bipeds and two-headed?

Answer

The question says ALL, so the two-headed circle surrounds the circle denoting bipeds. The answer is choice d.

More Than Two Categories

Should there be more than two categories, proceed in the same way.

Example: Some candy bars (c) are sweet (s), but no bananas (b) are candy bars.

The sweet circle will cut through the candy bar circle. Since the problem did not specify where bananas and sweet intersect, bananas can have several positions. The banana circle can be outside both circles completely:

The banana circle can intersect the sweet circle:

Or the banana circle can be completely inside the sweet circle but not touching the candy bar shape:

Hot Tip

Even when there are no pictures of Venn diagrams in the answers, you can often solve this type of problem by drawing the diagram one way and visualizing all the possible positions of the circles given the facts in the problem.