A Venn diagram is a good way to represent a syllogism visually.
A syllogism, one of the most basic forms of logical reasoning, uses two premises to reach a conclusion. For example: All dogs will go to heaven; Lucky is a dog; therefore, Lucky will go to heaven. You can represent a syllogism visually using a Venn diagram, which is a simple diagram that consists of two circles. You determine the extent to which these circles overlap–if they overlap at all–by considering the relationship between the two premises and the conclusion of the syllogism.
1. Analyze your premises to determine which two types of things they compare. For the example, consider “All dogs will go to heaven” and “Lucky is a dog.” What are the two categories at hand? In this case, they’re “All dogs” and “Living things which go to heaven when they die.” These will be represented by your Venn diagram’s “circles.”
2. Draw out your circles to reflect the relationship between the premises. For example, since “All dogs will go to heaven,” you can place the “All dogs” circle completely inside the “Living things which go to heaven when they die” circle, keeping in mind that the former should be smaller (you can assume the the total number of dogs is less than the number of total creatures which go to heaven when they die). Make sure your inner circle is touching your outer circle along one of its edges.
3. Draw a point or dot to represent your conclusion. For the example, you would draw a point inside the “All dogs” circle–which is completely inside the “Things which go to heaven when they die” circle–and label it “Lucky,” as Lucky, like all dogs, will go to heaven when he dies, according to your conclusion.
4. Label the insides of your circles with other examples of each category. For example, you might put the names “Penny,” “Biscuit” and “Rocky” inside the “All dogs” circle and “Cats,” “Houseplants” and “Sharks” inside the “Things which go to heaven when they die.”