Video: Using Venn Diagrams to Decide Whether Conclusions Are Valid

We can use Venn diagrams to model conditional statements. Which Venn diagram models the following two statements? [A] If an animal is a fish, then it lives in water. [B] Dolphins live in water. Use the Venn diagram to determine whether the following statement is valid: All dolphins are fish. [A] Valid [B] Not valid

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Video Transcript

We can use Venn diagrams to model conditional statements. Which Venn diagram models the following two statements? A) If an animal is a fish, then it lives in water. B) Dolphins live in water.

After we choose the correct model, then we’ll determine whether the following statement is valid: All dolphins are fish. But first, let’s pick a model.

We have the condition “if an animal is a fish,” the conclusion is that “it lives in water.” We need a Venn diagram in which all of the fish live in water. In this first example, we have a large group of fish, but only a small group of them live in water. The way this Venn diagram is drawn some of the fish fall outside of the space that lives in water.

We see the same thing in this third option. The space outside that lives in water is a space where fish would be that will live in water. This Venn diagram also places dolphins outside the water, which is not a valid model.

Our second statement, statement B, says dolphins live in water. Here is what these two statements are telling us: if an animal is a fish, then it lives in water. So we can say fish live in water. We also can say that dolphins live in water. However, we cannot say that dolphins are fish. We don’t have that information. We’ve just been given information about where they live.

Both dolphins and fish live in water. But just because dolphins live in water does not make them fish. We would choose the model that has both dolphins and fish living in water, but does not include the dolphins in the fish category. Based on this information, how would we categorize the statement “All dolphins are fish”? This statement is not valid. Dolphins are not fish. However, they do live in water.

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