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.