#7

Question

Write a conditional statement for this Venn Diagram.

It is a poodle if and only if it is a dog
A poodle is a dog
If it is a poodle, then it is a dog
A dog can be a poodle

Answer 1

The conditional statement that corresponds to the Venn Diagram you've described can be framed as follows:

"An animal is a poodle if and only if it is a dog."

This statement indicates a bi-conditional relationship: being a poodle is both necessary and sufficient to being classified as a dog. Here’s how you can break it down:

1. If it is a poodle, then it is a dog. (This shows that all poodles are dogs.)
2. If it is a dog, then it is a poodle. (This indicates that all dogs in this context are poodles.)

Thus, both conditions together articulate that the only dogs we are considering are poodles, and the only poodles are dogs.