Watch this video lesson to learn what categorical propositions are and how you can turn your statements into one of the four standard forms. Also, learn the names of these four standard forms and what they look like.

## Categorical Propositions

**Categorical propositions** are statements that tell you how one group relates to another group. For example, the categorical proposition, ‘Some cars are blue,’ tells you how one group, cars, relates to the other group, blue. It tells you that some things that belong to the group cars also belong to the group blue.

This is just one example of a categorical proposition.Also, in categorical propositions, the first group is called the subject and the second group, the predicate. We can label the subject with an *S* and the predicate with a *P*. In our example, ‘Some cars are blue,’ the subject is cars, and the predicate is blue. There are four standard forms that we can use to write our categorical propositions. Let’s see how these standard forms differ from each other by talking about our blue cars.

## A Form

In the A form, all of the first group is included in the second group. We write this as ‘all *S* are *P*.’ For our blue cars, we would say, ‘All cars are blue.’

## E Form

In the E form, none of the first group is included in the second group.

It is written as ‘all *S* are not *P*.’ For our cars, we would say, ‘All cars are not blue.’

## I Form

The I form, ‘some *S* are *P*,’ tells us that some things in the first group also belong to the second group. Relating this to the blue cars, we would say, ‘Some cars are blue.’

## O Form

The O form, ‘some *S* are not *P*,’ tells us that only some of the first group are not part of the second group. Applying this form to our cars, we would say, ‘Some cars are not blue.

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## Lesson Summary

What did we learn? We learned that a **categorical proposition** is a statement that tells you how one group relates to another group. These two groups also have names associated with them. The first group is called the subject and the second group, the predicate. For example, the categorical proposition, ‘No cars are pink,’ has cars as the subject and pink as the predicate.

We label the subject with an *S* and the predicate with a *P*. This kind of labeling allows us to identify the four standard forms easily.The four standard forms are the A form, the E form, the I form, and the O form. Using our labels for the subject and predicate, the A form is ‘all *S* are *P*;’ the E form is ‘no *S* are *P*;’ the I form is ‘some *S* are *P*;’ and the O form is ‘some *S* are not *P*.’ For our pink cars, the A form would give us the categorical proposition ‘All cars are pink;’ the E form gives us ‘No cars are pink;’ the I form, ‘Some cars are pink;’ and the O form, ‘Some cars are not pink.’

## Learning Outcomes

Reviewing this lesson could prepare you to:

- Characterize categorical propositions
- Label the subject and predicate of a categorical proposition
- Recollect and distinguish between A, E, I and O form