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Mathematical Sets Elements Intersections Unions Cardinality Types of Subsets (Infinite Finite Equal Empty)Categorical Propositions Subject Predicate Equivalent Infinite Sets What is a Two-Way Table

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GRE General: Venn Diagrams Subset Disjoint Overlap Intersection Union
Categorical Propositions Subject Predicate Equivalent Infinite Sets

Watch this video lesson to learn how categorical propositions are written. You will also see what the subject and predicate are as well as learn about equivalent and infinite sets.

Categorical Propositions Subject Predicate Equivalent Infinite Sets

Categorical Propositions

Categorical propositions are statements that show how one set relates to another set. For example, the statement, 'All rabbits are long-eared,' is a categorical proposition as it tells us that the things in the first set, rabbits, belong in the second set, long-eared.

In this lesson, we are going to talk about the subject and predicate parts of a categorical proposition as well as equivalent and infinite sets. So, let's get started with the subject and predicate parts.

Subject and Predicate

Because a categorical proposition shows how one set relates to another, we label these two sets the subject and predicate. The subject is the first set, or the main set, of the statement, while the predicate is the second set where the statement says how the main set relates to this second set.

In our statement, 'All rabbits are long eared,' the subject is rabbits, and the predicate is long-eared. Do you see how the statement tells us how the main subject set, rabbits, relates to the second set, long-eared? The statement tells us that everything in the first set, rabbits, belongs in the second set, long-eared.

There are a total of four ways that a categorical proposition can relate the two sets. We can categorize them easily, but we first need to label our subject with an S and our predicate with a P. The first way is called the A form, and it is written as 'all S are P.' For our rabbits, the phrase would read 'All rabbits are long-eared.' The second way is called the E form, written as 'all S are not P.' The phrase for the rabbits would be 'All rabbits are not long-eared.' The third way is the I form, which is 'some S are P.' For the rabbits, it would be 'Some rabbits are long-eared.' The fourth way is the O form, which reads 'some S are not P.' The phrase for the rabbits would be 'Some rabbits are not long-eared.' These are all valid categorical propositions and show the different ways our two sets can relate to each other.

Equivalent Sets

If our subject and predicate were the same sets, then we would have equivalent sets. It would be like us saying, 'All rabbits are rabbits.' Similarly, the two sets {1, 2, 3} and {1, 2, 3} are equivalent sets because they are the same.

Infinite Sets

The last set that we need to talk about is the infinite set. An infinite set is a set that goes on forever. Usually, these sets involve numbers that go on forever, such as this set: {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …}. Sorry, but there's no infinite set of rabbits that I can tell you about here. Just remember that infinite sets contain elements that go on forever.

Lesson Summary

So what have we learned? We've learned that a categorical proposition is a statement that relates one set to another. The two sets are called the subject and predicate, with the subject being the main set and the predicate being the second set. The two sets relate to each other in terms of what part of the subject belongs in the predicate.

The four different ways that the subject and predicate can relate to each other are A form: all S is P; E form: all S are not P; I form: some S is P; and O form: some S are not P. Equivalent sets are sets that are the same, and infinite sets are sets that go on forever.

Learning Outcomes

After reviewing this lesson, you should have the ability to:

Display your knowledge of the meanings of a categorical proposition, subject, and predicate
Specify the four different ways that the subject and predicate can relate to each other
Illustrate equivalent sets and infinite sets